IIRC, the /c/ was already changing to a palatal “ts” or “ch” preceding /i/ and /e/ around Caesar’s time. And of course all of this changed in different localities at different times, so you’d have to go back in a time machine in the first place to find out! 
Not in the Empire, but close enough to trade is Georgia, which does grow a very decent tea.
If you were going back to live in Rome, you’d have to content yourself with always remaining a plebian, no matter how rich you became. Romans were very conscious of bloodlines.
Anthracite has the best idea so far with the calculators… Except you wouldn’t even need the calculator. Math with Roman numerals is so difficult, there were actually shops that would sell the answers to multiplication problems, which they had tabulated behind the counter. One shop might specialize in multiplication by twelve, for instance, and another shop in multiplication by eleven. The clientele was small, but well-funded (engineers and architects).
Armed with a (modern) elementary-school education and a sandbox (to “write” down your work… I don’t think chalkboards were used, and paper or the equivalent was expensive), you could make a killing as a calculator. Patronage might still be a good idea, since the other calculatores probably wouldn’t like the competition. Find a wealthy contractor who wants his own personal math consultant, though, and you’re set. Nobody else need know.
If we’re insisting on bringing back material goods, by the way, your best bet is probably aluminum. Even if they didn’t recognize it as a precious metal, it’s an extremely useful substance, and would have novelty value if nothing else.
Hell, forget the calculators. I would guess anyone with a basic knowledge of math would do very well as a Roman Accountant type. Multiplication, division, etc. becomes insanely easy when done with arabic numbers as opposed to roman numerals. You could just make money with a high school math education!
Bring morphine…
…to ease YOUR pain.
Most useful: Knowledge… of how to make everything from painkillers to eyeglasses. And knowledge of what you know about the area you will be living, and what is most likely to be supported.
Certainly, if your want to thrive, or become famous and wealthy, just remember that those things (as we now know) are probably more burdensome as they come with GREAT risk.
Least risky is to mimic the success of a moderately successful merchant, etc.
What did others do to succeed then…at the merchant level? At the scientific level? Mimic and slightly exceed these types of successes and you can help ensure your own success, without standing out too much.
Think of your knowledge of math, science, food prep, med conditions, etc. All will give you an edge, provided you fit in first.
I am amazed that no one thought of making gunpowder and/or explosives. Could you imagine the power you would have? Just one demonstration of the multiple uses of tnt would have revolutionized the Roman world. No more battling with crappy swords and rapiers. The warfare would be, as the firework label clearly states, “light fuse and get away” 
Be a roving minstrel. You probably have hundreds of popular melodies in your memory, and if you could form a partnership with a poet who was fluent in classic Latin, you could be a Superstar with your vast repertoire of “original” songs. Since they didn’t really have much in the way of musical transcription, and no recordings, you might even avoid creating a time paradox.
As I suspected, language seems like it will be the biggest hurdle. I guess salt is out as a means to raise some funds, but other spices sound promising. I don’t want to bring back any obvious anachronism with me, so guns, calculators, and stainless steel knives are out.
My basic plan seems to be sound, though. I was thinking to try to pass myself off as a foreign merchant then once I became established, I’d work as a scientist/mathematician/inventor and go down in history as one of the great minds of all time. Jetavian Jaguarius would be remembered alongside the likes of Archemedes, Aristotle, and Isaac Newton (who of course would now be remembered for heading the rocket team that landed the first man on the moon in 1687 :)). My degree is in Aerospace Engineering, so I probably have a pretty good grasp of science and mathematics.
“Inventing” gunpowder is a good suggestion, it would greatly benefit the military which might enable me to get a high-ranking patron to fund my research. I’d also like to invent the hot-air balloon. (I’m actually surprised it wasn’t invented earlier. To think that humans have observed smoke rising from fires for thousands of years, and not once did it occur to anyone to try to capture some smoke in a bag to see if it would lift it.) Imagine what the Roman Legions would be like if they employed firearms, explosives, and aerial reconnaissance and bombardment. 
I wonder if a steam engine could be made with the technology of the time…
There was a thread, however, that basically said the Romans didn’t want steam engines or labor-saving devices - an inventor was turned away when he told the Emperor about his plan to build something along those lines. There were legions of slaves. Why build a steam-powered crane when a hundred slaves could do the same work and keep out of trouble? If you build a steam-powered crane, you make those slaves obsolete. They aren’t gonna just disappear. They need jobs. Most of the slaves are slaves for crimes they committed, too - would you want convicts running your delicate machinery?
But they’d be all ears for military hardware, I suspect.
What Squish said about always being a plebian has got me thinking.
If you went back posing as an important foreigner from somewhereorother, presumably you wouldn’t even have the status of a ‘plebian’ Roman - you wouldn’t be a Roman citizen at all. Which, as I understand it, could have alarming implications as far as your legal rights were concerned, at least as compared to actual Roman citizens.
So, how much of an issue would this be? And would it be possible to pass yourself off as a ‘real Roman’ from out of town? I know that the Empire had the habit of passing out Roman citizenships to important citizens in conquered nations as a way of keeping them loyal. Could you simply turn up in Rome saying ‘Hi, I’m the son of the Mayor of RedNeckistan in Outer Mongolia and I’m a Roman citizen’ or would you be sprung almost immediately as an impostor?
Required reading if you are planning on bringing back firearms*
- they don’t make posters like that anymore… which may be a good thing.
Well, since other people have suggested math and gunpowder, I’ll move on to my 3rd and 4th backup suggestions. To start with, one word…
Paper.
Or, more precisely, the knowledge on how to MAKE paper. Sure, you might end up with a deforestation problem once your business took off, but you might be able to find a more “eco-friendly” paper recipe.
And there’s another “Discovery” that you might be share with the Romans…the Americas. Just memorize Columbus’ course, find a good ship and some suicidal crewmen, and convince whoever’s in charge of the empire to make you prelate of any and all lands you discover for mother Rome. Then, once you get back, you can start your own Roman East India company and corner the market on coffee and cocaine (Or whatever other goods you can pillage-er, “trade for”, that can’t be found in the old world). Hey, if you’re feeling merciful, and you have a humane enough Roman leader, you might even be able to prevent the disease outbreaks and slave trade that started after Columbus’ little jaunt.
Of course, at this point, you’ll have royally screwed up the established timeline…Oh well. Shift happens.
Ranchoth
Keep in mind that wine was in universal use throughout the classical world, not because of its intoxicating or soporific effects, but because of its sanitary effects. Alcohol kills germs. Even watered wine was much, much safer than drinking pure(?) water. Therefore, if you’re selling coffee or tea, tell your customers to get the water to a full rolling boil for a full 5 minutes or they’re likely to end up with dysentary or cholera. Actually, I think most of them will find wine to be easier.
And to clarify the thing about salt–>salary–>income, Roman soldiers were paid in Roman money, just like everyone else. In addition to the coin (usually kept “on the books” by the legion’s clerk), soldiers were issued a monthly ration of useful items, foodstuffs and so forth, including salt for cooking. One’s “salt” became a common ironic reference to what the soldier earned each month, every month, and thus entered the modern parlance as a flat amount paid each month. Of course, salt was then, as now, very cheap.
And, has been recommended before, don’t guess at the circumstances until you’ve read deCamp’s Lest Darkness Fall. Extremely well researched, extremely well thought out. My wife, who as a linguistic scholar, speaks classical Greek and Latin in several different dialects, was very impressed with deCamp’s use of vulgar Latin in the 6th Cent. CE.
Bring a transistor radio, and if things start looking a bit dodgy, turn it on and amaze the ancient peoples with music!*
*This glaring piece of idiocy brought to you by Disney in their movie “A Spaceman in King Arthur’s Court”.
Although several folks have mentioned L. Sprague de Camp’s excellent book Lest Darkness Fall, I have to point out that his hero, Martin Padway (Paduei after he got there) was surprised by what worked and by what did not. Like his predecessor, Hank Morgan in Mark Twain’s A Connecticut Yankee in King Arthur’s Court, the dream of going back into the past and showing off using “modern” inventions turns out to be much more difficult than it at first appears. Few people seem to realize that Twain was making fun of his Yankee, as well as of King Arthur’s Court.
In deCamp’s book, Padway tries to make gunpowder, but he can’t get it to work. He tries in interest the Roman army in a (mechanical) telegraph, but they’re not interested. His biggest successes are distilling brandy, and the use of double-entry bookkeeping. He eventually starts a newspaper, but has to invent modern paper (as opposed to papyrus). He is helped enormously not by his knowledge of paper (he doesn’t really know how it’s made), but by his knowledge that paper can be made. This prompts him to experiment until he can find a way to successfully make the kind of paper he needs.
So you can, in principle, survive in Roman times. I note that Padway was successful enough to be able to hire a cook/housekeeper and a bodyguard. If he had to do it all himself, he wouldn’t have time for anything else (kinda like Frontier House).
“Therefore, if you’re selling coffee or tea, tell your customers to get the water to a full rolling boil for a full 5 minutes or they’re likely to end up with dysentary or cholera.”
You have nothing to worry about, since the customers wouldn’t be boiling anything in my plan. I’d be selling tea and coffee as finished beverages in a chain of coffeeshops, not as bags of tea leaves or ground coffee to be boiled at home. (Just call me Starbuckius ) Lots of Romans in the big cities didn’t HAVE the ability (ovens, hearths, etc.) to cook at home in their little apartments; that’s why even the lower classes had to eat out.
That got me thinking…I think the only thing that I’d bring is
a modern ‘well detailed’ map. I’d never let anyone else see it, but I’d be a freakin’ GOD to those guys with my knowledge of the continents.
[Enter two Plebians]
Testiculus: Have you seen that new store near the Forum?
Bolux: What, ‘Starbuckius’? Run by the guy with good teeth, bad grammar and a bizarre accent?
Testiculus: Yeah.
Bolux: What does it sell?
Testiculus: Boiled leaves.
Bolux: You’re kidding, right? Who the hell would buy boiled leaves?
Testiculus: I haven’t a clue. They also sell crushed beans in hot water.
Bolux: What do they do with this stuff?
Testiculus: They drink it.
Bolux: Why the fuck would you drink hot liquids? Does it get you drunk?
Testiculus: No, it gives you a very mild buzz, and it tastes like shit.
Bolux: I’ll stick to wine myself. That guy Starbuckius sounds like an asshole.
Testiculus: Let’s go and burn his store to the ground, wantonly.
Bolux: Nah, not tonight: they’ve got bread and circuses down at the Coliseum. Wanna come?
Testiculus: I’d love to, but I’m broke. Can you loan me some salt?
[Exeunt]
If the Romans will eat fermented fish sauce heated in the sun for days (garum), they’ll drink boiled leaves and crushed beans for sure.
Whatever you do - do not invent gunpowder. If you could convince the authorities of its value, you’d be a permanent guest of the emperor. Unsupervised, you might sell your invention elsewhere or risk being kidnapped or killed by enemies of Rome. Roman authorities might just decide that judicious torture would 1) prove you’re not a spy with an ulterior motive 2) get the gunpowder recipe (and how much do they need you then?) and 3) make sure you’re not keeping any other bright ideas to yourself.