I have several different rifles chambered in 6.5 CM, all are accurate enough with factory ammo, although all factory ammo doesn't make the best groups in all of the rifles. If you're shooting factory ammo at medium game, I'd suggest trying a box of 129 grain Hornady American Whitetail, as it has produced the most consistent
accuracy between multiple rifles for me.
Your budget will dictate the amenities, but at the low cost end, under $300, I prefer the Mossberg Patriot to the Savage Axis. The Wal-Marts near me sell the Savage Axis for around $270 and the Mossberg Patriot for around $300.
It is probably harder to find a rifle chambered in 6.5 CM that won't shoot than it is to find one that will shoot. If you're not in a hurry and keep looking around, you're likely to find some deals. As is always the case, how a rifle fits and feels to each individual is probably the most important consideration, since a rifle that doesn't fit the shooter and/or doesn't feel good/right to the shooter is a rifle that the shooter is never going to be happy with. I got a great deal on a Savage Axis in 6.5 CM, $215, but I have never liked how it fits or feels, so it was put somewhere to gather dust.
