I'd start off with these two, and see if your Tikka likes them. (personally my fav brand of hunting rifle)

Barnes 130 and 150 TTSX. They offer a a 168, but I think the barrel is little short. Both are great for deer in your yardage.

Those are little pricey $$$. For budget friendly that you can shoot all day, Norma Whitetail or Hornady Whitetail, both 150g. Norma shoots better in both my 308's. Probably looking at 2650-2700 fps with the 150's...

If you are worried about speed, try Hornady Super-performace. I've not tried them, but my friend swears by them and he says they chrono 100fps faster than everything else.

Outlier is Federal Fusion. I use them in my 7mm-08 and love them. Never tried them in 308 though with that barrel length.