Do whatever you want with most of them but
for gods sake save the rare ones. Or sell them at a good price, not to some shitty game store! Depending on the games you can get a LOT of money from them, so don't give them away for shit money to EBgames or whatever! Their value will rise with age, so if you keep them for a few years you'll make some good money off of them assuming you know when to sell them - and also assuming they actually are rare games people want.
"that may not seem like much when they sell them for $25-$50+, but you are NOT going to get that much back"
Worst advice ever. Check what you can get for the games, and don't sell them for any less. There's always a good place to sell it on the internet if you can't figure anything else.
As for what to buy? You're going to buy a DS Lite, with a flash cart, and then you're going to download all the games. YOu know what the DS lite costs, and a flash cart plus memory stick won't cost more than 50-60$. After that you're not going to pay for a single goddamn thing ever again for your DS. The
R4 Revolution works wonders, I don't think it plays GBA games though, so that's a bummer, but I can't recommend any other cart since I haven't tried any other cart.