We bought an Arcade, used it for 2 days before we had to buy a hard-drive. Many things (that they don't even mention on the game boxes sometimes) are completely unusable without an HD. Forza 3 for example, has loads of content (cars and tracks) on an additional disk which has to be installed direct to HD, you also can't view replays without a HD.
Ended up buying the 60GB LIVE Starter Pack, found that cheap at the time so didn't end up really losing out thankfully.
Another annoyance (particularly with Microsoft games) is that you need to be a Gold LIVE member to access quite a bit of stuff. I assumed Gold was just for actually playing online, but with Forza you can't access leaderboards, set up custom one player races, use the marketplace or anything like that without Gold, you can't even download free content you get with the Limited Edition version of the game.