Hi, Beth. Your approach is exactly right. Start by stripping the paint. I like environmentally safe strippers like Citristrip for many reasons. Glob some on the paint and wait for it to bubble, craze or lift and scrape it off with a putty knife. Don't try to brush back over the stripper to make it smooth and use a cheap, wood handled, natural bristle brush to apply. If the surface of the beams are rough, you might find that a stripping pad or brass brush are easier to use for removal. Remember that the stripper will remove the paint from anything that it touches so use plenty of masking tape around the beams and heavy plastic drop clothes on the floor. Now for the most important part--since you will be working overhead, be sure you wear gloves and full surround eye protection, a long sleeve shirt and a hat. The stripper mentioned is non-toxic but will give you a nasty chemical burn.
When you have the beams stripped, come back to the board and we'll try to give some direction on refinishing. It really helps to know what is under the paint first though.