I’ll second many of the excellent recommendations above. Here are a few other suggestions.
It’s good to find a solid, reasonably affordable all-rounder blended Scotch. JW Black Label is excellent. Something like this can work as a more affordable, everyday drink.
It’s also useful to get a sense of how good scotches can get by tasting some of the pricier ones. I’d recommend finding a bar or restaurant with a decent selection and sampling a half dozen or so. If the bartenders knows their stuff, they can give you recommendations, especially if you tell that what you like or dislike about the ones you’re trying.
The good news is that while they can get ridiculously expensive, single malts don’t have to be costly to be good (although they’re probably better suited to a weekend treat). Speysides tend to be quite sweet and smooth and easy to like. The standard Highland Park is very nice, as is Aberlour, which is my favorite. Among Highland scotches, Macallan is a popular option. Islays, as the resident connoisseur and expert @pennstac notes, can be more of an acquired taste, or have a taste that is more divisive. Besides Laphroaig, you might like to check out Ardbeg, which seems popular, to judge from the above posts. I’d try the last two in a bar or restaurant rather than risk buying a whole bottle.
Japanese whiskies are well worth exploring, too; the Nikka Coffee and Hibiki Harmony are deservedly popular.
Bourbons tend to be sweeter than Scotch, although they can vary considerably in their taste profile.
There has been a crazy explosion in bourbon’s popularity over the last decade. Previously cheap bourbons have become more expensive, often if they’re seen to be coming from the same distilleries that produce infamously expensive, fancy bourbons. For this reason, Buffalo Trace, which was once a perfectly decent, entry-level sipping bourbon costing around $25 in NJ (not a cheap place for booze) has now become $40-45, largely thanks to its association with the silly, overhyped craze for Pappy Van Winkle. The same thing can be said for the same distillery’s Weller brand, which is now very expensive and hard to come by.
There are also a lot of terrible bourbons out there now, with people trying to cash in on the current fad. Many are truly awful. Beware of folks in liquor stores trying to unload godawful stuff on unsuspecting customers. It may not work out well for you if you ask for a recommendation! I’d suggest starting out with some of the more well-known brands but do please steer clear of Jim Beam or Jack Daniels (the latter being Tennessee whiskey, which is its own, separate thing, and best described by some wag as “old tennis shoes”).
Some bourbons are spicy, as with Bulleit, which I don’t like but many do. I prefer Noah’s Mill, which is much more expensive but not as harsh, and it has an appealingly complex flavor.
My favorites are sweeter bourbons like those produced by Knob Creek. I also like ryes as a sweeter kind of whiskey. My favorite is Knob Creek, again, which represents decent value when on sale, while Elijah Craig’s is very good, too. Michters makes very nice, sweeter whiskies in the $40-50 range. They offer a solid bourbon, a lovely rye, and some fun other whiskies, including a Sour Mash one and an American Whiskey (not a bourbon or rye). You could have fun sampling all of them.
My favorite bourbon is Booker’s - which is a treat for holidays and special occasions.
Here’s a fun “bourbon family tree,” which appeared in GQ magazine a while ago (here):
The sweet spot for me, in terms of price to performance, lies in the 4- to 10-year offerings. Ones I’d recommend that I haven’t mentioned previously are W. L. Weller, Maker’s 46, and some of the Willetts.
This book is a useful reference. I’ve found that its recommendations make sense, even if I don’t like them, particularly, and the descriptions of the flavors are usually fairly reliable.