It actually depends on the size of the PS3 and I'm pretty sure when it was made. I'm not an expert thought, my dad did basically the same thing... Midlife crisis and all. As a result, I'm not sure of the size of my PS3, but I do know that is IS backwards compatible.
However, some models ARE NOT backwards compatible... I think newer ones aren't.
I'm pretty sure it connects to the internet, like 99% sure, but my dad keeps messing with the internet so we can get it OMG!faster, and so any attempts I make to connect to the internet with ANY of our consoles result in DURRP GOTTA RESTART AND ENTER PASSWORDS THAT ARE KEPT COMPLETELY SECRET but yes, there is an internet browser option.
ETERNAL SONATA. IS AN AMAZING GAME. It has bonus content not on the 360 version, it is a BEAUTIFUL RPG with amazing music... Sometimes the dialogue is a little weird and there is one scene in the game that is just plain awful, but regardless, I love it. Ending made me cry. Please support the company, please buy this game. Also, it has a fantastic battle system in my opinion. It's also fairly easy, which I like. Only one real side quest that I'm aware of, and fairly short, but I'd say well worth it.
Valkyria Chronicles is also a great strategy game. It's during a war but it doesn't give off that sort of "war game" vibe. This one's also pretty and fun. Battles can take up to an hour or so, but in between each battle is a good chunk of plot/general character antics. It's a very character driven game, which is always nice I think. 8D Battles are, however, very difficult at the beginning and do require a bit of strategy and exploration. If you're impatient, it might not be so awesome for you, but there are a lot of extras and other fun things. I haven't beaten it yet but it's pretty fun. It's become kind of a cult classic.
Sadly, those are the only two PS3 games I've played... My library is rather unimpressive... But I'm really looking forward to White Knight Chronicles, and I've heard good things about Disgaea 3, but I'm not too big on Disgaea's battle system and I spoiled the ending for myself, so I couldn't tell you personally. Oh, and Tales of Vesperia is being ported to the PS3 with new content, but we're not positive that it's going to be localized.