I went with a combination stain/polyurethane @Brioski. The only brand available where I live that's a combo stain/polyurethane is this one: Varathane. I got it at Home Depot in the paint department. They have several different color options. Some have a satin finish whereas others are gloss. I'd go satin .
If you want to know the specific process I used, shoot me a PM and I'll give you a step be step description. My concern with your project would be the kind of wood your accordion doors are made from. Most I've ever seen are either plywood or a thin laminate over plywood (to keep them light for opening and closing). If that's the case with yours, it may be tricky sanding them and then applying a natural wood finish. Plywood or laminates don't take well to heavy sanding then depending on the wood grain once they are sanded, how will they look with a natural wood finish? From your comment above I assume they are currently painted?
Like I said earlier, feel free to shot me a PM with whatever info. on your doors that you have - pic would be great too! I'll do the best I can to give you recommendations.
Here's my big coffee table after 3 coats of finish with a light sanding between coats. One more coat tomorrow, a light sanding and then an application of paste wax & ... it's done
