If you want a semi auto then get a heavy barrel AR 15, like this one:
http://www.snipercentral.com/rra.htm
If you want a bolt action, I'd go for a heavy barrel Savage or CZ.
Depends what degree of accuracy you want and what price you want to spend.
Personally I'd take a Savage or the Rock River.
Theres plenty of other choices out there though, my advice is search google A LOT, you'll find a heap of info.
Oh and if your after really good accuracy not just good enough then the mini 14 is not what your after.
I'd go for an AR if I were you, the Rock rivers are reasonably priced and you can get it in a Wylde chamber meaning you can shoot top notch match ammo, and cheap as dirt 5.56 ammo. You can shoot tight groups or just blow your ear drums out.
Also has plenty of accessories available, and you can buy a new upper for a different calibre.
They also come with great two stage triggers.
But do your own research, google is your friend, you'll find all you need to know and then plenty of stuff you didn't.