Specialized Bikes

$500 will get you a good hardtail but NOT a full squish (full suspension) bike. Those start at about $1,500. The difference between SRAM & Shimano components is all personal preference. 6 of one - half dozen of the other. Both good to great.
I would worry more about the strength of the rims & hubs. Insist on a bike with both double walled rims and a cassette type hub vs. the cheaper freewheel hub.
See all the real bicycle shops in your area. Google ‘bicycle shop’ and your zip code. Extensively try as many as possible. The one that feels best & rides best to you in your price range is the bike to buy. Seen a Raleigh Talus 4.0? 2010 models - $450 or maybe lower on a close out sale. 2011 models - $460.

Hardtail for sure. Most bikes at a similar price offer similar components. Visit a few bike shops and test ride a few to see which one feels best to you.

$500 i would suggest to save some more money at least $1000 before looking, however if you want to only spend 500 and are keen to do it soon, I would deffinatly have a look at giant they are good value for money, trek tend to be pretty over priced at least in the DH market i find they are.
As mentioned it is best to have a look around at all the stores you can to find out what you want.
It seems you want a all mountain/trail type of bike you can have some fun on, if your not sure, work out what type of riding you will be doing, this will greatly help yourself and narrow down the options a little. Tell the bike shops what you want and have a good look around at a few and then get on the internet and have a search of the bikes they reccomended. Research and knowledge is your best friend when buying a bike, it will let you know what you are getting and wont let you get sucked into the sale. I would say for that budget you will be looking at a hardtail deffinatly. Dont go for a cheap dual suspension for that price.
Get a sit and ride on as many of the bikes as you can, the feel of a bike is the best guide for you to find your perfect bike.
As for the sram vs shimano it wont matter too much with your budget, when you begin getting into the high end components the basic observations against the two are these:
-sram is stiffer and has a nicer snap reaction to changing gears, that is it is very quick and direct.
-sram deraileurs tend to break a bit more and shimano tend to have a little bit more flex in them which prevents them from snapping quite as easily.
personally I run all my rear gearing and deraileurs with sram and cranks I would run shimano.
you dont need to worry about sram vs shimano for your price range.
Your main goal is to find out what you want from the bike, and type of riding you will be doing, then shop around, dont be too worried about sram vs shimano, just focus on the main things like your frame and suspension.
hopefully that gave you some direction in where to go now with your purchase,
goodluck