Welcome to the sport. First, are you using open sights or a scope? I find scopes hard to use for thick woods and close shots; I have quick-release bases on my scope and remove it when I go in the woods.
250 grain-range bullets are a good size for deer. I use 195 grain Dead Centers, but you can't go wrong with 240-250 grains.
For close shots like you describe, there is no real reason to spend all the extra money on Dead Centers/Precision Rifle bullets in general. Maybe some of their cheaper hollow points, but no the poly-tipped bullets.
I have killed 20+ deer with the Hornaday 240 grain HTP. That or the XTP would be a good bullet to start with, they shoot well in a large number of guns. It will also kick less than a heavy Powerbelt with a similar powder charge.
I would suggest Triple Seven loose powder. All pellets are expensive and limit the grain charge you can use. Loose powder lets you adjust it to your gun. Triple Seven is, by far, the easiest of the powders to clean out of your gun.
For each bullet you want to try, start at about 60-70 grains and shoot 3-shot groups, moving up by 10 grains each group. At some point you will likely begin to lose accuracy. Back off 5 grains and try again to determine which charge gives you maximum power and still maintains accuracy. If it kicks too much for you, you can always reduce the charge a bit as long as you are in the accurate range. You MUST repeat this for each type of bullet, each will probably shoot well at a different charge.
