It really depends on what games you want to play.
You can buy a separate harddrive for your XBox 360, but it's going to cost you a lot of money, and it would be cheaper to just buy it with the system in the Pro package. But if you're not planning on playing a lot of games or downloading a lot of things, then sure, you could go the way of the Arcade... but you'll need some kind of memory unit for saving game progress eventually.
And if you find one someday that there's a game on XBox Live Arcade that you want to download, well, you're pretty boned without a harddrive.
If you're not into shooters, you'll hate Left 4 Dead, and you'll most likely hate Gears of War 1 & 2 as well. I wouldn't even bother playing shooting games on the 360, anyway, I find they are much more fun on the PC. But that's all a matter of opinion!