A harddrive isn't bad to have if you fancy downloading videos and demos. You can get a generic 250g with the Slim enclosure for 40-50 bucks on Amazon. Don't bother paying three times as much for the Microsoft brand variant unless you absolutely have to have buggy emulation of Xbox 1 games. A rechargable battery pack for 20 can also be handy, although the double AA's your 360 came in will likely last you 30+ hours so it doesn't have to be a top priority.
As for games, there is tons to choose from. For 20 bucks each you can get:
Elder Scrolls 4
Fable2
Fallout 3 / Fallout new vegas
FF 13
Grand Theft Auto (GOTY edition is 20 at walmart, 40 everywhere else atm. Regular edition is 20 everywhere)
Ghostbusters
Halo 3
Gears of War 1 and 2
Dragon Ages Origins
I'd suggest paying 10 more and getting the GOTY edition of Fallout 3 and Dragon Ages for all the add ons, but if the console and accessories is setting you back, the regular editions still give you a lot of value for your money.