You can get a 30.30 in a Contender but not a 308 or .270. Have to step up to an Encore for the higher pressure cartridges. I've done quite a bit of hunting with Contenders in handgun, carbine, and muzzleloader form. My favorite set up is a 6.8 SPC and its killer on whitetails.
For factory cartridges in a Contender, you're limited. A good .223 load would work great on antelope at moderate ranges.
For Wildcats, the sky is the limit. The JDJ family of cartridges have some real performers. The 6mm TCU(necked up 223 basically) is popular and would be a great load. I had a really accurate 7mm TCU BUT never could get reliable expansion at lower velocities with 7mm hunting bullets.
I've never seen one but I'd assume a 6.5 Grendel would be okay in a Contender frame. It would be a custom shop barrel I'm sure.
If you go with an Encore frame would could shoot anything you wanted to. I prefer the smaller Contender frame tho.