I work a lot on antique homes and the first thing I would encourage you to do is determine what kind of doors you have. There was a trend for awhile to paint over nice hardwood and if this is the situation you have you are in luck and your stripping efforts should pay off nicely. I have come across some gorgeous old oak pocket doors and staircases that were painted over, for example. You may be able to strip the doors just with sharp scraping tools depending on how much paint is caked on. If you are really lucky there will be a nice coat of original varnish to which the paint never stuck that well. Taking them off will make them easier to work with.
If you find that your doors are some sort of softer wood like pine or other conifer and that they were always painted, you are likely to be disappointed with your stripping and refinishing project if your goal is to return them to natural wood and stain them. You will never get them to look decent---at least from my experience. You might still want to strip them to get their details back if they have layers of paint but don't be hopeful as far as having a natural wood look.
You don't have to do so but especially if you find you have nice hardwood, I would strip or scrape the door trim too.
Do consider redoing the door hardware when you do the doors especially if the hinges and knobs are vintage. You can get them sandblasted and even plated for not a whole lot of money. Here is one company I have used for this but there are certainly folks around you that would offer similar services.
http://www.albarwilmette.com/
Do be careful with paint strippers and use with adequate ventilation. The older types are explosive and the vapors are heavier than air so travel along floors toward pilot lights and such things. The newer paste and gel types work well and are safer.