I got mine several months ago, when there still was a waiting list to get one. Because of my work schedule, my mother picked it up for me at the Apple store. They had activated it the Apple store. No computer needed on my part.
I jail broke my iPad via jailbreakme.com. No computer needed. (I know, that was an exploit on how safari handled PDFs and it was for 3.2 only, but....)
Having a computer does make managing your iPad easier, but it is not a requirement. I'll even bet that if you walked into an Apple store, they would install iOS updates for you.
Internet. If you are talking about 3G, the answer is no. If you are talking about Internet at home, the answer is yes.
The new Mac Book Airs are sweet. You could use the Air to manage the iPad, and for when you need more than a tablet. Just sayin...