Xbox – What memory stick should I get for the XBox 360

The cheapest option is definitely going to be the USB route as mentioned by others.

Ignoring the fact that Microsoft's hardware prices are inflated and overpriced, if you go strictly off a cost per GB, then buying the console with the 250GB drive is your best bet for the money. Using the averages prices these days

GB    Total $    $ per GB
250   $100.00    $0.40    (w/console)
250   $130.00    $0.52    (standalone drive)
120   $100.00    $0.83    (standalone drive)
60     $70.00    $1.17    (standalone drive)
16     $20.00    $1.25    (USB Drive)

I would assume the standalone drives have a warranty of their own, and the one with the console would be part of the console warranty, but I'm not sure on those.

Yes, that should have more than enough space for that. I've had my Xbox 360 for close to two and a half years, and after playing 100 or so games my profile takes up about 10MB. As for save games, I'm not sure how much space mine are taking but most save games are less than 1MB so there should be plenty of room for them as well.

If you do need more room and don't want to spring for the 250GB hard drive (now or later - it is cheaper to buy it with the console, though) you can always use USB drives for storage. The Xbox 360 supports drives up to 16GB.

Note that the vast majority of games don't require a hard drive, but some do. The only ones I'm aware of off hand are Halo 3, Halo 3 ODST, and Halo Reach. In this case, you can play the game but you can't play the campaign or Firefight in co-op mode (at least online - not sure if the same restriction exists for local co-op).