Hi Kay,
Any non-weight-bearing exercises might be good for you. If your local town rec center has a pool that might be an option as recreation centers tend to cost much less money than a commercial fitness center. A stationary bike might be an option, although you should try it out first to make sure it's okay for the knees. It will be an expense up front, but it will pay off long-run. Lots of the large retail stores like Wal-Mart, Target, etc, have reasonably priced bikes. You could try an elliptical as well since although it's weight-bearing, there is no pounding on the knees, and it's a great workout. You could also check out
www.collage video.com Give them a call and describe your situation and they'll make a recommendation.
You should probably check out exercise tubing for resistance exercise. Tubing is inexpensive and versatile (you can do lots of exercises with them even in a chair) and a great way to get started with resistance exercise. You can start with a set of three for about $20. They come in colors to denote the tension. If you order them make sure to order the strap that allows you to attach the tube to a door (this is essential for many exercises), and if you want to work your legs, ask for leg straps. Here are some vendors that sell them.
www.performbetter.com/catalog/default.asp www.power-systems.com And here's a site with great videos
http://www.body-mind-strength.com/resistance_tube_exercises/resistance_tube_exercises.html As for strengthening your legs/knees, I recommend straight leg raises. To do them lie on the floor on your back, one knee bent, the other straight, hands palm down under the buttocks to support the low back. Contract the quadriceps on the straight leg, then raise leg to the height of the other knee. Pause 1-2 second at the top, then lower leg but do not allow it to touch the floor. Repeat 10-15 reps, 3 sets. You can use ankle weights if these are very easy. Start with one pound and work up. You should always be able to do 10-15 reps. As you get stronger, you may be able to progress to leg extensions, leg curls, leg presses, squats, and other exercises. Here is a picture of straight leg raises.
http://www.webmd.com/osteoarthritis/joint-injections-9/slideshow-knee-exercises (slide #3).
Then click on the next picture which describes how to tighten the quadriceps before lifting as I instruct above.
Good luck! Rich