Seems like a decent deal. If it's a Leopard, it's 125cc, not 80. Not a huge deal for a kart to bang around on, but something to keep in mind if you're looking for parts. If there's a local kart track, go to a race or two to find out what shops support the track in case you need parts. It looks like an older Birel, but you should still be able to find parts.
Agree with the above that you'll want to use race fuel and good two stroke oil. Again, if it's a kart track, the local shop can sell it to you. Expect $11-15/gallon in 5 gallon containers. MG reds are great for learning as they don't wear as long.
If you do it, you'll need safety equipment. Auto race suits don't work as they're not skid resistant. You should be able to pick up inexpensive kart suits on Ebay. You'll want a full face helmet (most tracks won't let you run without) and Snell rated. Snell motorcycle helmets is what my son always used because they had a larger eye port and he could try on different ones at the local cycle shop. You'll also need gloves and some tracks require high top shoes. Wrestling shoes are a cheap option. You may need, at least, a foam neck brace as a requirement for the track, and it helps with the g-forces. Since both of you are starting, I'd recommend a rib protector, too. Especially if you and your son are different girths.
Before you get it going, check all of the nuts and bolts. They will work loose quickly. Most have holes for safety wire or are setup for safety clips.
Clean the carb after 4-5 sessions and before you store it.
A stand isn't 100% required, but it helps a ton when pushing the kart from your car/truck to the grid and when you do have to work on it. Again, a local track will have someone selling old equipment.
Battery is just a standard 12volt like you can get at any battery store. Keep a trickle charger handy to keep it topped up.
I'd offer him a grand for it to see if he bites, but $1200 is a decent deal just to get started.
Oh, and as EDT said, there's no balance shaft so get ready for it to feel like it's shaking itself apart when you're driving. That's part of the fun.
-Rob