As a first gun you say..... i'd steer clear of the .17 rem, and the 22-250...!!!!! what are you looking for the said rifle to do.... whats its primary use...?
if foxing.... i'd go .223, proven, popular, accurate, cheap factory ammo to cut your teeth on....
As a bunny gun.... no.... i'd go for a cheap and cheerful .22lr
and get a .223 for foxing long range bunny fun.
think of what you need it most to do and take it from there.... 22-250 will be an expensive bunny gun, and you won't get any benifit of meat, bar for ferrets.....lol
Snap.