I had both my knees replaced in August, 2008 and am very happy with the results. Both were bone-on-bone and one was bowed about an inch and a half due to severe arthritis. Now I'm completely pain-free when I walk!
You're very smart to be thinking about exercise now to get ready for the surgery because the better the shape you are going into the surgery, the easier the recovery will be for you. I was able to stand unassisted and play air hockey for 15 minutes with the physical therapist a few days after surgery and never used a walker once I got home (I didn't need it in the hospital either, but they yelled at me if I didn't use it
). I only needed a cane for the stairs for a few days. Everyone was pretty dazzled by my progress, so I felt like exercise really paid off.
My doctor and I had a goal of me being in the best possible shape going into surgery, so I did about 90 minutes of exercise every day in the months before leading up to the surgery date, divided between strengthening and cardio. I belong to a gym, so all the equipment I needed was there.
Cardio was important for calorie burning, but also helps with building a strong oxygen delivery system, which is important for healing. For cardio, I generally did about 30 minutes of high intensity intervals on an elliptical, which was the least painful for my knees, and about 30 minutes of recumbent bike. I found that moving the seat back on the recumbent bike helped my knees when they were painful.
I did both upper and lower body strengthening. My doctor encouraged me to focus on building up the muscles that surround the knee to create a kind of internal knee brace for post-surgery. Because one leg was weaker than the other, I did as many exercises one-legged as possible so not to let the stronger leg dominate. I did one-legged leg press, squats, leg extensions, and leg curls. I also did traditional squats, lunges and hack squats to the extent of my comfortable range of motion. My goal was to have Quads of Steel!
Upper body strength is also very important and your goal should be to be able to lift your body weight just with your arms. Sit in an chair with arms and pretend that you're in a wheel chair -- you want to be able to lift your butt completely off the chair by pushing up with your arms. You'll need this upper body strength to get in and out of a wheelchair in the hospital, get out of bed, use a toilet with grab bars, etc. You'll be surprised at how much you need to haul yourself around with your arms at first! Even now, I still need to be able to lift my body weight with my arms to get out of a bathtub or get off the floor because I can't kneel.
I did all the traditional upper body workouts, focusing on the main muscle groups of chest, back, shoulders, biceps, and triceps. Pullups and pushups were great because they're compound exercises that work a lot of muscles at the same time. Building up your bi's and tri's with arm exercises like curls and dips will help with pushing yourself out of a wheelchair. Ab and lower back work will help you strengthen your core and give you a strong foundation for learning to walk all over again.
You're also right that losing some additional weight will help with recovery. Since every extra pound that we carry puts four pounds of stress on our knees, you'll be thanking yourself post-surgery for every pound that you get rid of ahead of time. Even at a normal weight, it was challenging to go up and down stairs at first, so I can't imagine how tough it would have been with extra weight. And extra weight will wear out your new knees much faster, so the lower your weight is, the longer your new knees will last. That's important to me because I'm relatively young (55) for knee replacements (thank you decades of obesity ) and I'm not anxious to re-do the surgery any sooner than necessary.
A great book to get before surgery is: Total Knee Replacement and Rehabilitation: The Knee Owner's Manual
Best of luck to you and let me know if I can help in any way.