MichaelH, First off if you dont know the exact correct way to check the length of the trigger pull againt your arm then get some help, this not only affects recoil as in scope eye but your accuracy ,especally off hand; it sounds like you feel its coming close. If you are over 5' 10" then the standard length is short, assuming normal arm length,a spacer or to added between the buttplate and stock will help big time.
The bullets; we are talking 3 different designs of bullet here; the one you want for pass through in all circumstances is the 300gr Gold Dot; I personally use the 250gr Gold Dot for deer exactly place it will drop them on the spot and thats what I want, I use the 300gr for bigger game it opens a bit slower and penatrates much deeper. The all copper bullets and the 300gr SW are also good choices for max penatration.
Recoil assuming correct lenght of trigger pull you will be able to tell the differance as it will kick a bit more, but every thing being correct it wont be a problem. Lee