EDIT: After rereading, it seems I breezed over the details. I’ll be a bit more specific.
If you’re looking for a gloss finish, a spray lacquer should do well and will dry pretty quickly. You’ll need a lot of thin coats to build up a nice base. The upside is you only need to wait a few minutes between coats. If you’re satisfied with the finish of it right out of the can, it should be dry enough to handle within an hour or two and plenty usable within a day or so.
If you want more of a mirror finish, it’ll take some more work, but it’s not too difficult. After a couple of days, it should harden up really nicely and takes to wet sanding rather well. Get a good few coats down and let it harden up. When it stops stinking, you know it’s hard. Then use a some 400 grit or so and wet sand it until it’s nice and flat. Try to eliminate any shiny areas. Then lay down another several coats. Let it harden again and reflatten it with 400. Repeat until it’s as thick as you like. Then after the last round of spray, let it harden again and wet sand with 400, 600, then 800. Then buff it up with some steel wool (000 or 0000). After you get a nice consistent appearance, put down a little polish or rubbing compound and go to it with a soft cloth. With enough polish and elbow grease, you’ll have a glass-clear and mirror-smooth finish.
Also, remember to use a mask if you’ve got one and try to keep some good ventilation. The fumes off of the stuff are pretty killer.