I’ve tried a few and so far, the ones I liked best were, unsurprisingly, Glenfiddich and Jameson.
So, what other whiskies might I like? When I say “whisky” I include bourbon, scotch and similar drinks.
Basil Hayden, because it’s not heavy.
Knob Creek, because it is.
You really need to be more specific, because Jameson and Glenfiddich are totally different flavor profiles.
What is it you like about each of them? Do you want something that is smooth, or something that gives a little fight? Sweeter? Smokier? Fruitier? Cheaper? A little guidance is needed here. Which whiskies have you tried that you didn’t like?
And be prepared to take all advice with a ton of salt, because we already have a disagreement: I think Basil Hayden sucks donkey balls.
I quite disliked Wild Turkey and Bowmore. At this time, I don’t know enough about whisky to make distinctions aside from “liked” and “didn’t like”. I figure that by sampling a few recommended ones, I might get a better idea. Maybe I should organize something analogous to wine tasting but a lot drunker.
Now see, being a novice to bourbon myself, I was so proud of myself being able to show range.
Go on then. Recommend something smokey and sweet.
Nothing wrong with Basil Hayden. Lots of people love it. It just isn’t at all to my palate. Knob Creek, OTOH, just shows what a little different aging and blending can do, since it’s basically Jim Beam done up nice.
To the OP: My guess is that you found Wild Turkey to be too strong and Bowmore to be too smoky/salty. Lots of truth in that. If you get a chance, try Wild Turkey Russell’s Reserve and water it down a little bit. As for the Bowmore, don’t try any Islay scotch except maybe Bunnahabhain, which is very atypical.
Some admittedly biased suggestions:
Scotch
Cragganmore
The Glen Livet
Macallan
Glen Rothes
Bourbon
Broken Bell
Jim Beam Devil’s Cut
Knob Creek
Four Roses
All of those are widely distributed, fairly inexpensive and pretty accessible to newcomers.
As for the Quicksilver challenge: Try a good rye. Definitely not your everyday whiskey. 
TX is a relatively new one that is made in Fort Worth. It may not have a widespread distribution yet. It’s pretty smooth with a vanilla flavor.
I’ll often choose Makers Mark because its easily available. Knob Creek from time to time, too.
I recently tried Woodford Reserve (?) but it was a little too harsh for me.
If you like Irish whiskey (which is what Jameson’s is), you might try Powers. It’s more full-bodied and flavorful, in my opinion.
It’s not quite as easy to find as Jameson, but it’s out there. And it’s no more expensive.
Nitpicky stuff – “whiskey” is the spelling of the word as applied to Irish and American spirits. “Whisky” is for Scotch and probably some others too (can’t remember how, say, Suntory spells it).
See if you can find a nice bar that offers “flights.” That way, you can sample several.
Powers is excellent for Irish & may be found in Houston. For Scotch, I like a bit of Laphroig (sp) occasionally; but it’s not for everyone.
For a bourbon, I’d recommend Bulleit. Their rye isn’t bad, either.
Seconded on The Glenlivet, and I also like Balvenie, for scotches.
Are you going to be sipping it neat, with ice, with soda, with Coke, making cocktails?
I tend to drink neat but if someone knows of a different way that’s worthwhile, I may try that. The only except is that I won’t drink it with any soda except diet 7up.
Whisk(e)y and soda is an Abomination Unto Nuggan, so you’re ok there.
Tully Mars mentioned probably the most accessible bourbon out there: Maker’s Mark. It’s a wheated bourbon, so the flavor is going to be smoother and more rounded. If you find you like it, move up a grade to Maker’s 46, which has the benefit of some additional time on oak.
Seconding the rec for Power’s in an Irish, and putting in a word for Bushmill’s as well.
Add Christian Brothers Brandy and Jim Beam Rye to your list.
CB Brandy leans more toward cognac than whiskey (same grapes but not made in France) and JB Rye is very smooth.
If you like Glenfiddich, you will most likely enjoy other whiskies from the Speyside region (including the forementioned Cragganmore and The Macallan, which are also two of my favorites – the former especially so). Other commonly seen Speysides include Glenfarclas and Glenfiddich.
As others have suggested, if you don’t like Bowmore then stay away from anything coming from the Islay region (Lagavulin, Laphroig, Ardbeg, Bunnahabhain, etc.) – they are noted for their extraordinary peat smoke character.
Unfortunately, that may mean that you won’t like my favorite Scotch whisky: Highland Park. It’s technically a Speyside, but from the Island subregion and it’s got more than a little peat character compared to other Speysides. I absolutely adore Highland Park.
Some other favorites of mine that haven’t been mentioned: Springbank and Old Pulteney – both of those are pretty accessible and easy to find.
I concur with the notion of going to a well-stocked bar (one that specializes in whisky/ey would be best) and asking for a flight. There’s a world of differences between Scotch, Irish and American whisky/ey, and I’d advise having different flights concentrating on each nation’s offerings (not all on the same occasion, of course).
You might also search for Scotch tastings in your city – many bars and restaurants will organize events that highlight offerings from a particular distillery or a range of brands owned by the same company.
And that’s just Scotch – while there’s not as much of a difference between Irish whiskies and North American whiskey/bourbon/rye, each nation’s spirits have a wide range of character. Even Colorado is producing its own distinctive whiskies (of which Stranahan’s is by far my favorite).
I knew I liked you for a reason! 
If we ever meet, I’ll share my Highland Park 20. It’s an independent bottling, so it got 2 more years in the barrel than the normal HP18. delicious!
I shan’t forget the offer. I think Highland Park’s whiskies are among the rare offerings that are actually worth the significant price point difference when buying older bottlings. The 18-year-old, especially when found on sale, is a great, great value for a wonderful whisky.
Definitely appreciate both of these, especially the rye notes in Basil Hayden’s. But my preference is Willett Pot Still Reserve, fancy bottle and all.
Highland Park and Talisker are my favorite more mainstream single malts.
You’re welcome.