That's a fun quick project.
If you're good with paint, I'd probably go with stencils, but if not a sticker would certainly be very easy and straightforward.
For the lid, I'd put one on, it makes a great play table and seat, but I'd use those Toybox lid hinges that are either gas damped or spring loaded to prevent the lid from smashing down.
http://www.rockler.com/search_results.cfm?filter=toybox&submit.x=0&submit.y=0I used that for my daughters toybox. The only way it'd slam down is if you forcibly slammed it down, and held onto it all the way down.
For the finish, poly would work, but this might be a good project to experiment with that super gloss pourable epoxy. I've used it on projects in the past, one pour is like many MANY layers of poly. and super tough too.
it's messy, though, so put down lots of dropcloths!
You can get it at lowes or home depot, but I can't find a link there right off.
http://www.rockler.com/product.cfm?page=21371&filter=pourable%20finishGood luck. My daughter helped me build hers. She was 4. Got a big kick out of staining and nailing...well swinging a hammer at least!