Squats or other kneeling exercises like lunges are great for activating a lot of the large muscles and for increasing stability in the lower legs. They are also good for working balance, especially if they are done on a wobble board or Bosu.
The caveat is that you really need to do them correctly or you will end up hurting your knees and also possibly your lower back.
The first thing to remember is to engage your abdominal muscles, (which is true for most exercises, but often forgotten). You also want to keep your torso long, by that I mean, don’t hunch your shoulders or let your rib cage collapse. Keep your shoulders relaxed and lift your diaphragm, while using those abs to stabilize your lower spine. F.Y.I. this is pretty much how you want to maintain your posture all the time, exercising or not. Try not overly tense the muscles around your rib cage, you should be able to feel your diaphragm expand and contract freely when you breathe.
The second thing to to is to keep your knees over your ankles or slightly in front; never let them go past your toes. Instead reach back with your hips while keeping your shoulders aligned over your knees. You can use TRX straps or stiff firmly anchored tubing for balance, or simply extend your arms to the front as you lower into the squat.
There is also a wall squat, or chair squat variation that you can do with a stability ball between you and the wall. Start with the ball right behind your lower back. Walk your feet out from the wall, so that when you lower, it looks like you are sitting in an invisible chair, back straight and knees over the ankles.
In a lunge position, whether stepping back or forward, your legs should look like two L’s. The front one facing down and the rear one facing backwards. Again, use straps or a band anchored to the wall and do reverse lunges if you need assistance at first. Then progress to free standing and forward stepping. As you adapt you can move onto an unstable surface for added challenge.
There are lots of variations and ways to keep these exercises challenging and fun, by using medicine balls, kettle bells or free weights, but get your basic mechanics down first.
If you have had injuries you definitely want to check with your Doctor before any exercise, and consider consulting with a Trainer, (like me!) for personal instruction on correct form, durations and repetitions.