If it puts the bullet where you are aiming, it will do the job.
I just posted the following to another thread, but it might help you, too:
I just stared deer hunting a couple of years ago. Didn't want to spend much money on a rifle in case I didn't like hunting. So I bought a $99 Mosin Nagant 91/30, installed a $40 scope, bought 20 rounds of ammo (7.62x54R... approximately .308) for $16 and have brought down two nice whitetails in the past two years. Both shots at under 100 yards, and I found out that I LOVE hunting.
Spend whatever you want on a rifle. Feel good about it. But there is no need to spend a lot on a rifle to put venison in your freezer.