Model 10? First pump shotgun Remington made. Easy to identify, has a flapper style carrier hinged at the side.
Model 17? JM Browning design, bottom feed and eject, takedown, the precursor design to the Ithaca Model 37.
Model 29? Bottom loading and ejection, takedown.
Model 31? Remington's first side-ejecting shotgun, looks like a steel Mossberg 500.
Parts are generally not available, if they are they are generally used parts with the same problems your gun already has, or used parts with a problem your gun doesn't have yet. Stocks are available pre-carved unfinished, expect to pay about $130 or more for a buttstock, $90 for a forearm, and put a lot of work into it.
If it was me, I would explain gently to the customer that it cannot be fixed for less than he would pay for a new 870 Wingmaster. I rebuilt a Model 10 a few years ago for a friend (sentimental value, it was his Dad's wedding gift from his new wife/my friend's Mom) and with new wood, reblue, straighten the barrel, and fix the carrier, he paid me $600 for the work and now the shotgun lives in a closet.