building a desktop (not a laptop) is pretty much the only way. you won't get a laptop that is worth the upgrade for that price.
probably:
($120) amd FX 4100 (i3s are a bit more expensive)
($125) Radeon 6770
($95) 500GB hard drive
($45) 500w/600w PSU (preferably spend $50 or more on this)
($18) 4GB 1333mhz RAM
($110) a Gigabyte AM3+ motherboard.
($60) Case
total: ~$570
EDIT: i forgot the operating system. you can either see if anyone has a spare copy of windows, but bear in mind that you'd probably want to upgrade to a 64 bit version of windows 7 as soon as possible, in which case you probably want a person who is still in full time education in your house, so you can get a (considerable) student discount.
as you can see, it's a bit over your budget. although you can probably cut down the price by $50 or so if you went for an AMD phenom X4 and a AM3 motherboard.
this spec would run most games out now on medium, maybe high settings if you push it a little, and would last a good 3 years playing games at that level, building a computer is something that i would reccomend doing if you want to know more about computers, and is not as difficult as you may think, especially if you have someone you know who has done it before.
on problem is that you won't have a complete machine warranty, and will have to find out what is causing the problem yourself if it breaks, and send off the faulty part back to be replaced accordingly.
you *may* be able to order it off somewhere like cyberpower, but apparently the build quality is so-so and you'll be paying for them to build it too....
another option is going for an i5 2500k and not buying a graphics card (use the integrated), then buying that later when you have more money to spend. it'll play legions and probably a few games like TF2 fine, (you might even be able to squeeze skyrim out of it) but bear in mind that some games do not support integrated (EDIT: legions is one of them ~*Fireblasto*), and it should really only be used as a stand in while you save for a better graphics card.
