Once you know what the camera is that will help answer some of the questions, Beth. Generally speaking, though, with an older camera I will open up the back and point the camera at a light source and fire the shutter at various speeds, looking for light through the lens listening for appropriate sounding changes in shutter speed. Sticky shutter on older cameras often manifest their naughty behavior at slow shutter speeds.
As to checking for light leaks, you might be able to see pinholes in camera bellows, again by opening the back and holding the camera to light. But the chances of you inheriting a bellows camera is probably small. (Although the "it looked neat" description is certainly tantalizing.)
Film: I'd shoot witha cheap color film first to test the camera. And I'd get the roll developed cheaply at Costco. After that, if the camera is working well, you will find that the different emulsions available offer opportunity to experiment and become acquainted with one look or the other. Me,...? I like Kodak Ektar for color print film, and I shoot a lot of Kodak Tri-X for B&W. Recently @
Chris Dodkin has been churning out some smashing images with slide film (Fuji Velvia).
Looking forward to finding out what you get.