One thing to have clear is that exercise, unless you are exercising at a very high intensity for more than an hour every day, does not provide much in terms of actual weight loss. There are tons of reasons to exercise, but from a specific weight loss perspective, it is not going to make or break the rate you lose weight. Unless, of course, you have time to spend hours working out, which most of us don't.
Once you've been medically cleared to lift more than 15 lbs (usually at 4 weeks, but check with your doctor), you are pretty much free to do any sort of exercise you wish. You should incorporate some resistance exercise (weights or bands or just body weight movements) to help retain muscle mass. Without it, some people experience significant muscle loss along with fat. No matter what you do, you will lose some muscle, but the goal is to minimize that and try to maintain at least 3:1 ratio of fat loss to muscle loss.
High Intensity Interval Training is highly recommended because it combines resistance training with cardio, and you don't have to do that much to get the benefits. 20-30 min 2 or 3 days a week. Of course you can do more. You can do intense HIIT at home with no equipment and get great benefits.
For general health, walking is hard to beat, but adding in resistance exercise during this rapid weight loss phase is very important. Some people seem to get a little concerned that they won't see the scale move as much if they are gaining muscle, but that is rarely an issue when we have fat to lose. It takes most people about two months to gain 3 pounds of muscle with regular (three or more days per week) of focused strength training. It usually takes most people much longer to gain that much muscle because they aren't just solely weight/strength training. The bonus resistance training and gaining muscle though is that your metabolism and fat loss will be better with more muscle, and it should actually help increase your overall weight loss. It will also help you maintain your weight once you reach your goal.
As you said, everyone has a different rate of progress, so continue to keep that in mind. Some people lose almost all of their weight in 6-8 months, and others take a couple years. Some people lose consistently, and some lose in spurts here and there in between stalls. There really isn't a "normal" experience from what I've seen reading what everyone experiences. There are "averages" of course, but those are sort of misleading because the actual experience each person has can be very different.
The thing to remember, and you have to keep reminding yourself of this, during this first 6 months or so, as long as you are following the basic guidelines, making good food choices, staying hydrated, maintaining a calorie deficit and adding in some exercise, you are always burning fat, and your body composition is changing, no matter what the scale reads. Your body goes through adjustments here and there, but if you are making good choices along the way, you will make progress.
Stay the course. Step away from the scale for a while and focus on building new habits.
