Sounds like you have a bit of work ahead. I have a few ideas that might help you, but without any spraying, finishing the doors will still be a lot of work.
First is the set up. I like to stain and finish doors when they are standing, in an upright position. The doors can be connected to each other with simple angle brackets. (Check out this page for more details – <a href="https://www.house-painting-info.com/painting-doors.html">Painting Doors</a>, about halfway down.) This will give you access to all sides of the doors.
Second, this deals with the staining. Use a lamb's wool stain pad or cut a ? inch lamb's wool roller in half. Use one of these to apply a wiping stain. It is faster than brushing alone. You will still need a brush for some areas.
Test the stain with one of these applicators on a piece of poplar and thin the stain if necessary for the best color. You will still need to wipe the doors down, but at least the stain application will be faster.
The application of a finish is still going to be time consuming. I highly recommend using an airless sprayer with a 310 tip.
Spraying really isn't very hard. Most mistakes are using to much pressure with a big tip. By using a small tip the pressure can be turned down, allowing you more time during the spraying.
If spraying is out of the question then try using a small weenie mohair roller, then lay off with a brush. This method is fine for varnish and most polyurethane's. Some acrylic urethane's can also be rolled. You will have to test this method with the finish you are going to use.
Everything else is the same. Sanding is best done with a fine sanding sponge. And a shop vac can be used before tacking. Then the second or third coat of wood finish is applied.