The PS2 is still a great system. It's so good, that it even outsold the PS3 over the holidays with
1.3 mil to 1.2 mil. The product support is still there, so you should be in good hands for now.
If you have a slim PS2, meaning it's smaller than a phonebook, it has a built in internet adapter. If you have an old fat PS2, which is about the size of a large phone book, you have to buy a seperate adapter that clips onto its backside.
Connecting to the internet for online play is easy. All you have to do is plug an ethernet cord into it, and you can play any online capable games from there.
Since you're tight on cash, I'd recommend shopping on eBay for games and accessories. Because it's an older system, you should be able to find stuff pretty cheap.
As far as next-gen systems go...
If you like playing online with other people, but don't want to pay for it, the PS3 is what you want.
If you don't mind paying $4 and change a month for great services, Xbox 360 is what you want.
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