Congrats on the win. Since you're getting the unit for free, your dad can get talked into all sorts of extras!
If it's a core system... get a hard drive for it immediately, don't worry about memory cards, hard drive takes their place.
Get an extra joyst.. oops, I mean
controller, for your siblings, friends, AND DAD! At least one, wireless or wired, but it's nice to have a wired in case you're batteries go dead in your wireless unexpectedly.
Get Xbox Live... the online subscription.. go ahead and spring for a year's worth.
Get a points card or two, so you can buy online Xbox Live games (5 or 10 bucks each is what they come out to, but the cards call 'em "points", so 400 points=$5.00, 800 points=$10.00.)
As for games, check out this topic:
Xbox 360 Essential Games List and find a game or two you like. Nice thing about the 360 is you can download demos of a lot of games right from your console and try before you buy.
Add me to your friends list, my gamertag is
mthrnite.
Buy Rainbow Six Vegas and get online around 9 PM eastern and look for me!
Oh, and don't mod your box.