I like the 7 mm Mag for deer, but as stated if short range many others will do the trick. One over looked caliber now a days is the 308, this would serve your purposes well and be easier on the pocket and recoil to shoot. Another very popular cal. is 3006 or 270. All are cheap to shoot and easy to find ammo. That being said if you want a 7 mag get one.

Bullet styles are all opinions and experiences. Personally i like BT, but that is what suits me and my situation. In tight the flat based bullets like parts or spire points would be a good bet. Just shoot a bunch and let the paper and your situation dictate what you throw down the pipe. IMO for deer almost any bullet type will work, given range and shot placement...just a matter of confidence and preference.