Congrats on the offer!
I hope things work out for you. In this market, some resorts can be almost impossible to liquidate so you are wise to seriously consider any offer you receive.
Here are a few bits of advice I hope you find helpful as you proceed. Some of it will simply echo Denise's post (but the warnings are worth reading again!)..
1) Try to determine if the buyer is truly an individual and not simply another reseller in sheep's clothing. Don't pay any more upfront money!
You've already paid Timeshares Only to advertise your property, any brokerages and resellers affiliated with them would earn a commission at closing and not require any additional up front cost to you.. There are numerous "resellers" and "marketers" who make low ball offers pretending to be a buyer, then when you contact, their offer somehow turns out to involve you paying them a fee. If the deal sounds shady- call TSO and ask to be transferred to one of their affiliated brokerages. You can get advice and closing company recommendations. If you get an agent who doesn't seem helpful, ask for someone in management to assist you with your questions. The offer notice you received should also contain a referral to one of their brokerages if you prefer email communication.
2) Get as much info as you can about the ownership transfer process and the related costs involved..
If your buyer isn't savvy- they may not know about these costs. Depending on what you own and the marketability of the timeshare itself, it may be in your interest to also consider paying for a portion of these costs if the buyer gets cold feet.
3) Contact your buyer as soon as possible! Be persistent!
Buyers will often make several offers at the same time for similar properties. Because there are normally far more sellers that buyers, if you snooze- you may lose out on the potential sale!
Again- good luck!