Putting Poly over vinyl is not a good idea
No matter the type of material used for the artwork, until the pores of the wood are sealed, any adhesive will have limited sticking ability.
I'd have the artwork done on quality paper, no coating or anything.
I'm gonna point out what I've said in order to clarify, as it seems even after re-reading it myself that I've suggested something else entirely.
The first part of that quote references any adhesive's sticking ability to the straight stain, as was spoken of prior to my reply. Wood has to be given some smooth finish that the adhesive can stick to (such as poly). Failure to do this will show that the pores and ridges of UNFINISHED wood do not make a very good surface to stick anything to, along with the actual stain being something that's not all that easy to stick something to either.
As for the rest of what I said, I continue to stand by it. The poly over
paper will give it the protection and finish to look good for years to come, and the ability to keep the edges from peeling up, or someone's kid with no concern for his cab to purposefully peel up the edges. The poly will make it far harder to do, and will help the artwork to "blend" into the side, being covered by several coats of poly. There may not even be a seam for anyone to feel (or pick at).
Anyone with an older cab that some knob in the arcade was picking at can vouch for the fact that people absentmindedly tear up stuff that they can get a fingernail at/under. Mebbe they've got the need to do a quick manicure or whatever. If it can't be covered with plexi (reasonably priced, anyhoo), such as a CP, I'd recommend the same thing every time. Nicks and scratches happen to the artwork no matter how careful we are. I'd ALWAYS rather have them happen to a poly layer than the actual artwork. I can simply lightly sand and recoat the poly and it'll be as good as new, but I can't say the same about the artwork. Some scratches may be deep enough that you can't do anything about it, but I know it can be much worse without the protection of a coat or seven of poly.
Varathane clear would be a nice choice (anything other than that labeled "clear" could color any white in the artwork, but they tend to primarily sell "clear", so it's not as commonly available in a big-box store)
If you're getting art printed, skip the paper route.. get it done on adhesive vinyl to start with ( if it's inkjetted it'll be laminated with a protective layer anyway).
Not being sure of who the OP can/would go to for printing, or what you'd consider a "protective layer", but if you're referring to an actual lamination being done by the printer, it's certainly not done by every printer. I know this because several others have brought this up, as well as my own experience, due to it being a separate/extra charge. If you're referring to the paper itself as it comes through the printer, I'd be willing to wager that you'd not want some yokel spilling something on it because it's not truly something that could be considered a "protective layer" because it'd ruin the artwork. Covering it with poly would allow you to run a friggen HOSE on the thing and not worry about ruining the artwork (everything else, however, now that's a different story
)