Please keep in mind that I have not done anything like your are planning to do. Everything I am about to tell you is based on what I have read on the boards here.
Restore jobs can be anywhere from fill-sand-paint (wood filler for small spots and bondo for larger areas) to full electronics troubleshoot and cap kits for the monitors. Cap kits involve replacing all the capacitors on the boards of the monitor. These are not for the faint of heart, some of those have large killing voltages if not handled properly, mainly the monitor.
First lets look at the guts of the machine. Does it turn on and play or are there problems with burn in (seeing an image on the screen without power) do the controls work as they are supposed to? If the machine boots up but the controls don't respond then this could be an easy fix. This could be as simple as reconnecting the controls to replacement. If the monitor is dim then you probably need a cap kit. If the internals are shot then you might want to consider gutting the whole thing and put in a computer with MAME.
Now for the exterior, leave the layer of stuff on but try to locate a new sticker set for the artwork. Take off the old artwork if it is a sticker then fix any blemishes to the woodwork and sand the whole cabinet and wipe off the dust with a wet rag until is comes off clean. Just sand enough to roughen up the coating and smooth out the wood putty / bondo. Then prime, wet sand 400 grit, prime wet sand 400, paint wet sand 600, paint. You could go another coat of paint if you feel it needs it just wet sand again prior to painting but don't sand after the final coat. Make sure you wipe down the cab each time you sand. You should get a decent paint job from all that work.
Now to restore the control panel depending on the current condition of the joys and buttons you could clean them up or replace them. If you want/need to replace check out GrovyGameGear or Ultimarc they have good prices on their parts. Another good place to look is eBay but be careful of the auctions there, look for sellers that have high feedback numbers and close to 100% positive feedback. They will even have an eBay store and almost exclusively sell arcade parts. You can get Happ controls quite a bit cheaper there then direct from Happ. You can also get lucky on the individual sellers with low feedback if you are careful. Set up a PayPal account if you are new to eBay because that adds a layer of protection to you the buyer. I recently got a hardly used Happ Translucent Blue 3 inch trackball for $56 at auction from an individual seller.

I have rambled on long enough. Get some pics of the cabinet as it sits now, both inside and out and post them here. That should get some attention from the regulars sooner than later. Good Luck on your restore.
TTFN

Kaytrim