Body weight exercises (e.g. lunges, squats, planking, sit ups etc) can be a good transition to fitness, as can gentle pilates. My PT specialises in working with overweight individuals and she swears by these methods. They can be especially useful if you have 'problem areas' (although my problem area seems to be 'all over'!!) as you can target specific muscle groups and notice a difference in your shape relatively quickly. When I reintroduced myself to cardio last year, we started with some shadow boxing and I found that great too - it's low impact but definitely gets the heart rate up. These are all things you can do in your own home too, without a PT. I'm sure there are lots of apps or you tube videos that can give you a routine to follow?
My personal thoughts are that the earliest you introduce exercise as part of your daily routine, the easier that maintenance should be once you're at goal, because you'll already be doing a big chunk of the hard work needed to keep the weight off.