Get Fat Princess as far as PSN titles go. There are a lot of great titles. I even bothered buying Mortal Kombat 2 for the nostalgic value of it. Do you have an Xbox 360? If so, don't re-buy any titles on the PS3, because that would be wasting money. Definitely pick up Uncharted (both old and new), Killzone 2 if you want a good shooter, and whatever else suits you. I own both consoles but I buy most of my games on the PS3, so I'm playing through Batman: Arkham Asylum and Red Faction Guerilla.
As far as your WiFi connection, check your encryption settings. Do you run other devices on your wireless network, like an iPhone or a laptop? Re-check all of the wireless settings. Even though it sees the network and adds it as your connection, it still may not pass encryption, NAT, or any other enumerated network function.
Hope that helps.