Welcome to TUG!
The first rule of selling a timeshare is never pay more than a modest listing fee (less then $50.)
If you pay the resale company several hundred dollars upfront, what's their motivation to ever actually sell your timeshare? - None! And you are right, the buyer does pay the closing costs.
Just so you know, this is a really tough time to seller a timeshare. With the state of our economy, resale prices have dropped to an all time low and there are many nice resorts for sell for $1, with no takers. Even many of the top resorts are only selling for 50% of their original price. You might be better off to keep your timeshare and learn how to get more out of it. If you decide to do that, you've come to the right place!
For lots of info. about how to sell your timeshare, see the article posted at the top of the board.