It comes with an Ethernet cable, you don't have to worry about buying one. You can leave the system any which way you prefer, there are no repercussions to leaving it vertical instead of, say, horizontal. I myself keep it flat down. There are several different types of rechargeable battery kits you can buy, depending on your style of play (i.e charge-and-play or a regular one that just charges when you finish playing). You don't need any extra accessories except for the charge kit and possibly another controller, if you really want one.
Install games that you're going to be playing alot on your harddrive, your 360 will be silent as a mouse and the disk won't even spin. Load times, etc will be alot faster, too.
So, you mainly like third-person shooters, racing and fighters?
Get Dead Space along with Gears 1/2, Forza 2/Burnout Paradise and check out Dead or Alive 4, Mortal Combat: DC Universe and Soul Calibur 4. Be sure to look out for Street Fighter 4 and Tekken 6 next year.
Don't limit yourself to the genres you like, though, because there's TONS of other must-play games on the 360.
oh, and congratulations!
Proud Owner of: 
250gig FFXIII SE Xbox 360, 250gig Xbox 360 S, black Wii, 120gig PS3 Slim, soon to be 3DS *___*
