"Reasonable time" is directly proportional to how pissed you'll be if they give it to someone else. I'm very happy for you that you got offered the job...but remember you're not the only one that applied. YOu are obviously their first choice...but don't be smug about it. Don't make them wait. If you want the job and are happy with what they're offering, call'em right up and say "you're my Daddy now!"
You've interviewed already, right? So now starts the negotiation. You've prolly done this a million times already but a little advice doesn't hurt.
*Ring-ring* ABC Company, Mr. Jones Speaking.
Mr. Jones, HI! This is Joe Blow, I just got your job offer in the mail and am absolutely elated!
That's great Joe, when can you start?
Well, Sir I really want to work at ABC, but I feel a little salary negotiation is in order.
He'll either say well, what did you have in mind? Or he'll say, look Joe, it's $5.15 an hour plus all the fries you can eat...take it or leave it...
Joking, but you get the idea. Just be polite about it all and GOOD LUCK!