After staining the doors, you'd do well to apply a clear coat to protect the wood.
One way to avoid brush strokes and get a nice glossy finish on the doors would be by using a Wipe-on polyurethane rather than one meant to be brushed on. Support the doors horizontally (by putting them on chairs, boxes, pails or something, and get a preferably white preferably cotton rag damp (but not dripping wet) with the Wipe-on Polyurethane:
(I don't know that it's necessary to apply the poly when the doors are horizontal. If you don't get the rag as damp, you could probably poly the doors in place. I think you'd still need to remove the hardware for best results tho.)
Wipe each door down, and store the rag in a Zip-lock bag in the freezer between coats.
Minwax Wipe-On poly is an alkyd based polyurethane, and as such is similar to all oil based coatings in that it absorbs oxygen gas from the atmosphere. There's nothing you can do about the absorbtion of oxygen when the rag is out of the Zip-lock bag. However, by storing the rag in a cold place, you prevent the oxygen absorbed into the liquid poly from reacting with the unsaturated sites on the alkyd resins, thereby preventing the cold liquid oil from solidifying into a solid. That way, your rag remains soft until you're finished using it. If your rag does harden, then just continue with a new rag.
Wipe-On poly is what amateur woodworkers use to get smooth clear finishes on their projects.