and that is an option if you want it, BUT, you can never go back to the original stain. The skin is too thin to sand it down and remove the paint embeded in the grain.
I think the doors will look good and it will brighten the area up with them painted. A few pointers: Use a semi gloss paint, this reflects the light and is washable, flat paint is not. First think wipe the doors with a cleaner to remove all the grease and grime especially around the handles. Then remove the handles. Now, with some fine grit sand paper, start sanding in the direction of the grain enough to just make the wood dull. I forgot, buy some saw horses and take each door in the garage to work on it. this is much better on your back and you will not spill paint on the carpet.
Now again sand on both sides and on the ends. You just want to rough it up. Repair any dents or divots with a wood putty.
Now prime the doors with two coats of a good primer, I recommend Zinzer BIN. Two coats maybe three, then after each coat has dried. apply your finish coat. Do two coats on it. Be sure to paint the ends and sides.
Let dry and re install. You might need to touch up after installation due to the banging of the door while installing the hinge pins. Just touch it up.