Look for independent bottlings. Gordon & McPhail do some nice ones. I have a Glenlivet 15 that is wondeful, and not an age they do themselves. Same same for a Highland Park 25.
Personal tastes are just that - personal. I can’t stand Islay malts (Bunnahabhain excepted) but I adore the Islands (Highland Park, Talisker.) You just have to search out the bounds to your palate. It’s a rough job, but you can do it!
For Bourbon I think my systematic approach might be a little different, because there aren’t as many geographic dimensions as Scotch. I mean, there’s Bourbon, and there’s Tennessee whiskey, and that’s about it for geographic distinctions. Even then, basically Jack Daniels & George Dickel are Tennessee whiskey, meaning they go through a charcoal filtering process before aging, and everything else is bourbon.
Within those, there’s a lot of variation based on mash bill though- the big two being high-rye, and wheated bourbons. Most bourbons are roughly 75-80% corn, with the balance (usually) being either rye or wheat. Rye gives what are called “spicy” flavors, while wheat is generally not “spicy” and is considered smoother. Something like Old Grand-Dad is high-rye, while Maker’s Mark is a wheated bourbon.
So what I’d do is lean into the differing mash bills, so I could see which one I liked more. Personally I’m a high-rye guy all the way; wheated bourbons are almost bland.
Okay, I’ve got my mind made up how to approach this. I’m going to buy many glasses before I consider buying a bottle and I’m going to try to pursue greater variety before pursuing greater preference.
I would first like to be able to recognize the major styles. So I’m asking experienced folks here for recommendations of what they think are the most representative examples - not necessarily the best - that possess a particular flavor characteristic in spades.
Peat?
Brine?
Fruit?
Smoke?
I understand there are many other types of flavor profiles (funny, I don’t recall ever seeing any advertisements selling up how strong of a Bandaid taste their brand has) but have to start somewhere.
Are you absolutely intent on making scotch your target? Scotch is very much its own thing. If you’re a complete whiskey neophyte I’d recommend trying a little of everything. You might land on scotch or you might discover that bourbon or rye or something else lights up your taste buds.
No, I’m not married exclusively to the idea of scotch. I can see merit to sampling bourbons and other types. What would you recommend as far as representative examples of other types of whiskey to sample? I’m hearing Makers Mark a lot here.
Maker’s Mark is boring, IMO. And as a wheated bourbon, not really representative of the vast majority of bourbons out there.
I’d actually go try something very middle-of-the-road like Wild Turkey 101, Four Roses Small Batch, or Old Forester for a good, solid representative of what most bourbon is like.
(Cracks knuckles) (IMHO) (YMMV)
Highlands - Glenmorangie (The largest selling single malt in Scotland, if that tells you anything)
Lowlands - Auchentoshan (Not my favorite region)
Speyside - Macallan, Glenlivet (These are what people with taste buds think of when they think of single malt Scotch.)
Campbeltown - Springbank
Islay - Bowmore
Islands - Talisker, Highland Park
A little heresy - try some blends before you dive into single malts. A little research will tell you what malts make up that particular blend, and will help you recognize what you’re tasting. Johnnie Walker Black, for example, uses primarily Oban, Talisker and Lagavulin malts in its blend.
American
Bourbon, wheated - Maker’s Mark
Bourbon, rye - Wild Turkey, Old Grand Dad
A HUGE number of the “boutique” brands of bourbon are basically MGP’s standard output, aged and blended by the bottler. Caveat emptor.
For people who think they don’t like Maker’s Mark - try the Maker’s 101. The higher proof gives the whiskey a bit more edge, so it isn’t the soft, unoffensive beast you know and loathe. 
Soft and unoffensive might be just what you want if you don’t already like whiskey.
Try drinking cheap scotch first. It is harsh and tastes like crap as far as I’m concerned. Then try drinking an aged single malt scotch. It’s smooth as silk in comparison.
I actually considered this. Providing extreme contrasts is one way of getting to know and appreciate what and where the differences lie quickly.
I’ll certainly second Glenmorangie, it’s quite accessible, without the heavy smoky/peaty flavors that turn virgin Scotch drinkers off. Especially look for any of their bottlings that are aged in wine casks. These are more on the fruity/honey side of the spectrum.
Ditto Balvenie Double Wood and Macallan Double Cask. Sometimes you want a sherry bomb.
Plasters may be shorthand for Sticking Plaster, what Brits call Band-Aides.
I checked and my Laphroaig is the 10 YO (ass).
I’ll put it aside for a couple more years and revisit
Especially if they’ve ever heard “Cabin Pressure”.
(BBC radio series with Benedict Cumberbatch, Roger Allam, Stephanie Cole and John Finnemore, who also wrote it. HIGHLY recommended!)
An old drunk that they put up with, because he always tips phenomenanly well, often gruffly yells “Where’s my Talisker?”
So I just had to try some.
I applaud this list.
ETA: I agree with Balvenie Doublewood, which might be a good starter.
If you have the opportunity to attend a whisky tasting at a local high end liquor store I highly recommend that. Go with a friend. Don’t expect to be driving home.
Usually the evening will focus on a specific distillery. It can be really interesting to compare the difference that age makes and what characteristics are typical of that distillery and region. Often there is a related blended whisky they might start with which can give some perspective also.
Sharing with a friend goes a long way too. Having someone else share the experience, whether friend or stranger can really expand the scope of what to look for and what you like.
Single malt scotch and Bourbon are vastly different creatures.
Whisk(e)y doesn’t continue to age in the bottle. Drink 'er up!
I’m not saying that we can’t be friends, but we won’t be sharing a bottle any time soon. My wife got me a bottle for some occasion and it tasted exactly how my grandma’s medicine cabinet smelled. 
I, one the other hand, have never met a Glen I didn’t like. Glenmorangie, Glenfiddich, Glenlivit.
Just FYI - I ordered me a pair of those Glencairn glasses yesterday. And I’ve got a bottle of 14 year old Glenlivet that I bought a month ago with some Christmas money that I’m just itching to crack open. (I wanted to finish off that nasty 8 year old Lagavulin first, but I may not wait that long.)