You can go online with the core pack and no HD - but you probably won't be able to download much. Even if you can download some of the files that're online, all of the demoes would simply be too big to fit on it.
Personally, I'd just jump for the Premium system - unlike the PS3, there isn't any essential hardware you'd miss out by just getting the Core system (unless chrome plated disc drives are a must have), but it's just more convinent, and probably cheaper, to get that and be done with it.
Yeah, in the long run you are better of getting the premium system since even with the core you would still need to buy a memory card. That is about half of the difference in price right there. Not to mention the wireless controller. Just spend that little extra and get the premium. Otherwise don't even bother.