It's hard to tell for sure because your camera isn't well focused, but based on what I see I would choose to polish it carefully with carnauba wax rather than clearcoat it. Once the game has a nice very nice layer of wax, you've considerably slowed any further damage to the paint. Then you can take your time planning a more perfect restoration with clearcoat in the future.
Maybe in the future you'll have a better opportunity to clean out the cracks without damaging the playfield. Anything you do to clean out the cracks should be followed with an automotive clearcoat as vid1900 suggested above. If you're going to use sandpaper on the playfield, I believe 600 grit is too rough. If you can find a store that sells auto-body materials, they should carry grits of 1000 and up. Using 1000 grit I can clear the high spots, and then follow-up with wax and get a very high gloss finish.