Well then a lever gun in 30-30, or even 35 rem, or in a pistol caliber woulld be fine. Not minding recoil? Then you can opt for 45-70, 444 Marlin or the like, but they can kick like a mule.

It's a bit more in price. (ok, quite a bit if new) but you can try outa T/C Contender or Encore Carbine.Several calibers to chose from, with the added benefitthatthey can be switched out to pistols when you are ready for it. I got my Contender pistol frame (not a G2) for $150 used, and a used barrel for $100 (if I remember right). New barrels are going to cost you anything from $200+ to $250, pistol or carbine, and a carbine stock is $50 and up.
I have mine in .22LR and 30-30 in 10" pistol barrels and a 7mm TCUin the carbine. I way even thinking of picking up a used 45-70 ported carbine barrel that was at a local shop. (and 'cause I like the big thunder, kicked by a mule, make everyone at the range say "what the heck was that!" type of guns)

And I have to admit I am partial to single shots. Makes you pick and chose your target more and it's (almost) all that I use anymore.