A lot depends on how much you want to spend, of course. As someone just getting started, I think you can get a lot of enjoyment in the $40-80 per bottle range without breaking the bank. It allows you to get a handle on what you like in terms of taste profiles (e.g., sweet vs. spicy, etc.) After that, you can always move up and start spending more per bottle on pricier stuff if you feel like it.
Stuff in that range that I happen to like would include:
Old Forester 1910
4 Roses Small Batch Select
4 Roses Single Barrel
MIchter's American Whiskey
Russell's Reserve Single Barrel
Pikesville Rye
Knob Creek 12
Woodinville
Redwood Empire Lost Monarch
FWIW, Larceny Barrel Proof (A 124 batch) just got awarded best in class in a big spirits competition, and you can still find that bottle in this range.
Store picks are often a good choice in my experience. Not always, but often.
There are also decent bottles below $40 if you are selective, but in general I think the $40-80 range is kind of the "sweet spot" for getting good value while still drinking something worthwhile.
Other people on this board who know far more about bourbon than me can chime in with additional suggestions.