What caliber to practice with?

[Norwegianwoods]

If I was you, I would bring the 308 and use that.
The chances for you making good killing shots with your 308 are much higher than if you shall borrow a more powerful gun you are not familiar with.
Specially when you are a bit recoil shy as you said.
Using a high quality bullet in a 308 will kill plenty good enough if you put it where it should be.

 

[TerryR]

The best strategy is to extensively practice with the rifle that you are going to use. That isn't always practical, certainly in this case it isn't, the best strategy then is to shoot a similar rifle enough times that you are not afraid of the recoil, and then practice extensively with a 22LR. Ideally the 22 should be a similar rifle to that which you are going to use, again not possible here as the closest action type to the Kgun is a traditional pump which cycles the opposite way. In your case I would shoot your 308 with 180 gr rounds regularly to stay accustomed to the recoil, frankly if you can shoot a 308 comfortably you won't have trouble with a 300 WM. I would also regularly use a 22 off hand to maintain focus on stance and trigger press. In my case I go to an indoor pistol range weekly and shoot 50 -100 rounds of 22LR. Shooting a 22 is the best anti flinch medicine there is. Good luck and enjoy.

 

[Rastaman]

I agree with the post above. Just shoot and shoot often. Shoot the 308 and then let it cool while shooting the 22, then shoot the 308 some more. Don't worry about the change in caliber.
More importantly, shoot free hand, shoot off sticks, sit down and shoot, shoot fast, lean against a post and shoot, get some animal targets and practice shot placement. When you have developed your rythym it shouldnt matter much what gun you put in your hands.