A finished basement can run from 8k to 15k if you do the work yourself. If you hire a contractor I'd put the estimate at 20 to 35k. Tack on another 5k to decorate and add security, to make it easier to rent and maintain.
I finished my 1800 sq. ft. basement for 12,500 in under a year on the weekends. Check out the website below, it's got some cool articles about doing it yourself. It's not for everyone but it was great for me.
Be sure to get the DC business license required for landlords as well.
If you find that you will need to eventually go below your old foundation to get the required ceiling height, get bids from an experienced contractor who has done underpinning in the past. And get a permit.
As far as demo or construction work goes, it pays to do everything by the book, with permits. This is because when you sell your house, you can actually claim the legal improvements in the listing.
If you're tempted to do everything yourself, I read somewhere (This Old House Magazine, I think) a convincing argument against being your own general contractor and in favor of hiring one. If you're the general contractor, all the liability is on you. If anyone working on your property gets injured, you and your homeowner's insurance are liable. Instead, get a construction attorney, all the permits and a general contractor, and let the pros do what they're good at.
Of course if you are a licensed contractor that's a different story.