I'd start with lower proof stuff. 90 proof or so. Avoid rye whiskey to start as they are a bit spicier.
Suggestions:
Buffalo Trace *
Weller Special Reserve (wheated)
Eagle Rare *
Hancock's Reserve *
Old Elk Wheated
Michter's small batch bourbon
Woodford Reserve or for more body get the double oaked.
Makers Mark
Knob Creek
Old Forester 1910
An Irish whisky would be Redbreast 12 (maybe slightly more expensive than the rest of this list but a very easy drinker)
*may be a bit more difficult to find on the shelf
I fully agree with @Ostatedchi on these more specific recs, especially Redbreast 12. Very easy drinking whiskey.
My favorite low cost and easy to find bourbon is Michter’s small batch. Woodford is probably even cheaper and easier to find, but not quite as enjoyable.