Don't buy any PS2 games as they will
not work in the UK, at least not unless you've had your PS2 modified and your TV can handle the display!
As for GBA stuff, as Jedi Jon has said, will work fine. We bought a Gameboy SP for my daughter ($70) and the games were, on average, $30 each. Considering that new GBA games in this country retail at £30 the savings to be made in America are considerable. Its the one time my kids have been let free in a video game shop and basically told, "choose what you want".
The value is even better when you look at 2nd hand games. We visited two
Electronics Boutique stores in the Orlando area which sold new and used games. They both had a very good range of titles and when the 2nd hand stuff is costing < $15 (well under a tenner) it's outstanding value!
The two we visited were at
Mall At Millenia and
The Florida Mall. Of the two, I'd reccomend the latter as the Mall At Millenia, whilst being nice, is very 'up market'. The Florida Mall is has more down-to-earth stores where as MAM has stores without prices labels, i.e. if you have to ask the cost, you can't afford it!