I looked at the Rem 260 and I agree. Much better ballistics than the 308. But ammo choices are limited and much more expensive than the 308. Given that, we'll keep our hunting shots within 300 yards and train, relatively inexpensivly, out to 500yrds.
Honestly, I'm huge fan of 308 myself...I was only throwing out the cartridges in case you were looking for alternatives.
For your applications though, 308 is more than adequate. 308 has a rainbow-like trajectory compared to some of the other calibers, so you'll have to be solid on your fundamentals when shooting at 500 yards and beyond. As you noted though, it is available in great abundance and usually at a good price.
The recoil is mild, but can certainly be mitigated with a suppressor or muzzle brake. I've never owned a Tika, but I've heard plenty of good things about them being reliable and good rifles out of the box (which means a lot nowadays with some of the less-than-stellar firearms that are coming off the factory floor).
All-in-all a pretty solid choice given your intended usage.
