The answer to your question all depends on where you hunt. If you live in open areas I would suggest a bolt action with a 3x-9x scope. If you hunt in the really thick stuff I would suggect a lever action.
I would say if you want an accurate deer rifle that's good for a 12 year old and under $500...
For the first scenario, let's say youhunt in an open area...
try this one out for size
http://www.remington.com/firearms/youth/700spsyth.htm

I would personally recommend either the .243 or the .270. Both calibers are very accurate and don't deliver much recoil. Notice though, that the gun I showed you is a youth model. If you plan on this gun lasting for many years, you may want an adult model. Either way, I would stick with a Remington. The synthetic stock will also cut down on weight and increase durability. Pretty much anything by Remington or Winchester will get the job done. If you want, Remington does make a pump action rifle that is around the $400 range.

If you hunt in an area with dense foliage I would suggest something like a Winchester model 94 Trapper
http://www.winchesterguns.com/prodinfo/catalog/detail.asp?cat_id=534&type_id=094&cat=003C

though it is on the smaller side, it provides a lot of power. You a caliber on that gun, I would suggest the .357mag or even the .44mag.

As for the action of the gun, I believe bolt action to be the most reliable and accurate.

For the best calibers of a deer rifle: .243, .270, 6mm, 7mm-08, .264mag.
In my personal opinion, any .30 caliber gun is an overkill for deer. But all the same, a .308 or .30-06 make good deer rifles as well.

If you need any more help just email me at [email protected]
I wish I could be of more help to you, but hopefully I have helped a little.

Mike