Below are my recommendations for beginners who are just getting into bourbon and don't want to blow a ton of money right away. Most of them should be pretty widely available. Prices vary nationwide, but most should generally be $20-25ish or less.
These are all high quality bourbons - some rated very highly by veteran members of this site - that are also great values. I can't guarantee you'll like all of them, but I think they will allow you to see the different styles of several different bourbon distilleries.
I have also included a rye whiskey recommendation for four of the five distilleries.
W.L. Weller 7 year old 107 proof
W.L. Weller 12 year old
Eagle Rare Single Barrel*
Elmer T. Lee*
Old Rip Van Winkle 10 year old 90 proof* (my top recommendation on this list)
Elijah Craig 12 year old
Evan Williams Single Barrel
Rittenhouse Rye Bottled-in-Bond* (100 proof)
Jim Beam Black 8 year old*
Old Grand-Dad Bottled-in-Bond* (100 proof)
Jim Beam Rye
Old Forester 100 Proof/Signature*
Wild Turkey 101 proof*
Wild Turkey Rye
* denotes a personal favorite
Veterans, please feel free to add similar recommendations to this list.