When I was shooting a 30-06 I was using Remington Accubonds with 165gr bullets. They performed well in my gun. In my 7mm Rem Mag, I shoot Hornady Interbonds.

The 06 will drop deer effectively with just about any round at that range. Experiment a little and find the bullet your gun likes best, as every gun will shoot different bullets a little more or a little less accurately than every other gun.

Depends what your rifle likes, there are many many options that are suitable. I peronally like 150gr Hornady Interbonds

If you put the bullet in the right place, any 30-06 bullet from 110g to 220g will kill a deer effectively out to 300 yards. For that range I prefer a 150g Hornady. I like the terminal performance of the Interbond (great penetration and little meat damage) but the SST is more accurate for me in that rifle. The 150g is relatively flat shooting to minimize holdover. My next choice would be Clay's 130g... plenty of whollop for deer and even more speed. The deer never seem to notice what it was that hit them; they just fold and die. Your biggest concern will be ruining meat and that is where I like the Hornady Interbond.

I think 150 grain bullets would do fine.