Alright, I'll answer some of your questions.
Hardware: Yes, the 60GB PlayStation 3 has built in WiFi, so you can have wireless internet.
The warranty is about $60 for one year, I believe.
Games: Resistance is a bit overrated in my opinion, but that's just me. Most people love it, so there's a good chance that you will too.
Right now, the only games that are considered to be very good are Resistance: Fall of Man, Motorstorm, The Darkness, Virtua Fighter 5, Oblivion, and Ninja Gaiden Sigma. Out of those, Motorstorm is my favorite, and I'm not even a huge racing fan.
There's not any must-have games out right now, but they're coming soon enough.
Online: Yes, it's free. Home isn't out yet, it should be later this year, though.
There are headsets, but they don't come with the PlayStation 3. I'll be getting a bluetooth headset, and I recomend you do the same. From what I've heard, if you buy the retail version of Warhawk, you'll get a free bluetooth headset. That's what I'll be doing if that's true.
Package: From what I remember, it comes with one controller, and all of the basic stuff. It doesn't come with component or HDMI cables, so you'll have to buy those separately.
TV: Yes, it supports up to 1080i I believe, could be wrong though. Obviously, the PS3 looks better on a HDTV, but it looks plenty good on a SDTV as well.
My guess is, you'll need around $700-750. For the system, a game or two, and possibly other accessories. I'd say you need at least that much, it just depends on how many things you want to buy.
Hope this helps.