Congrats on the sale! That said -- don't be sad if things fall through. I've gone through several web site sales over the last year and they have all been terrible, frustrating procedures.
You seem to be past most of the hurdles, but there are a few things to remember --
Make sure the contract spells out a maximum time you will spend assisting them in transferring the site to their servers. Some companies see your availability at the beginning as free labor for the site and will try to milk you for months running the site for them.
Get all the information you can on the people and company you're dealing with. I mean things like personal cell phone numbers and addresses and things. It sounds invasive and wrong right now, but when it's 2:00am eight days later and you're still wondering when he's going to tell escrow company to release the funds to you, it's good to have a backup-backup-backup means of getting in touch with someone.
Document everything you do. This is going to be a great learning experience for you.
Even if the person you meet on Thursday has experience buying web sites in the past, that doesn't mean he's not a dumbass. I recently sold a site to a small company that owns a few surprisingly large web sites. It turns out the owner has no idea how to run a web site. He didn't even know what PHP, MySQL, FTP, or a "shel script" is. He talked a good game until it came time to install the web site on his server, and no one in his office (it's about a six person operation) knew what to do. (He thought the solution to everything was "cPanel.")
Drink a lot of water. The stress you're going to go through over the next few weeks will take a toll on you. Your brain needs lubrication, and works best when it and your body are well hydrated. You need your brain to be alert at all times.
Be nice. Be honest. Don't let him take advantage of you.
If you see something that makes you uncomfortable -- walk away. Don't let the lure of all that money force you into making a bad decision that you'll regret later. I once almost sold a web site to a guy who turned out to be a hard-core spammer. He wasn't interested in the site at all, but in all of my heaps of user data, and was likely going to shut the actual site down. He offered me a metric assload of money for the property, but I ended up walking away from that deal, and to this day I feel good about it.
Make sure what you're doing is legal. I know that sounds silly, but depending your circumstances, it can be problematic. For example, your web site could be running on software that isn't allowed to be exported to companies in the nation in question. Or you may have to document (for your own records) that the company you're selling your site to isn't doing business with companies in another nation that your government deems hostile.
As the guy you're meeting with if you can record your conversations. Some people don't like this, but if you're meeting in a conference room in a business center they're usually more comfortable with it. I like to have everything recorded because I can sometimes skip or miss small details and will want to go back later to make sure I heard something right. You don't want to screw this up.
Good luck and keep us posted on your progress!