Legs are huge calorie burners.
Most of us find leg exercises the easiest. There are tons: walking, running, squats, lunges, machines at the gym, biking... so many choices. It's easier to find something that you like or, at the very least, find tolerable. Legs are usually where you'll see the quickest results because unlike other parts of the body, they're engaged many times throughout the day. If you get adequate steps in for the day (recommended is 10k) and do a few strengthening exercises, you'll see some kind of progress within a few weeks.
I was always in fair - good shape, but when I started to turn up the intensity at the gym, it took me about 2 weeks to see a difference, 3 to feel stronger, and about 4 weeks until my calves were impressively taut. Mind you, I've always been pretty active, so I was not starting from scratch. However, when you go from nothing to something with exercise, you tend to see results a little quicker (think of the first few weeks of Biggest Loser-- huge numbers in a short time that taper off to more gradual changes and smaller numbers).
As I'm sure you know, it takes more energy (aka calories) to maintain that new leg muscle you have. And what that means is that since it takes more energy to maintain the muscle, you're calorie expenditure at rest will be greater. Yes, you read that right. Just by giving yourself a little extra muscle, you've increased the amount of calories you burn just by being alive.
When I increased the intensity at the gym, what I did was something like this: (1) Started with the legs. Out of 3/4 gym days, 1 was an intense leg day, and the rest were walking/bike and beginner core and upper body exercises. Saw results within about 2 weeks. Legs got stronger, could stay on the bike longer. (2) Once the legs were set, shifted leg exercises to maintenance-mode, and upped the intensity with core and upper body. (3) By 6 weeks, saw real changes in body composition.
By "upped the intensity," I mean that I did more than 2-3 exercises each day. I've worked myself into a routine that now that for each region of the body that I'm working on that day, I choose 6-7 exercises. I'm not an intense gym-goer by any means; I just moved from very basic to more than basic.
Moral of the story: If you want to start an exercise routine, start with your legs! If you have a lot of work to do (based on your own opinion and assessment), then start with just increasing steps and standing more for a few weeks to get your gams used to it, and then move on to some leg exercises. Go from there. Results won't be instantaneous, but if you're like me, you'll see something encouraging within 2-3 weeks. The hardest part is getting over the fact that you may not notice the changes as fast as you want. For me, I didn't notice anything..... until I did. It felt sudden, but one day I looked in the mirror in my underwear and thought, "Um, I look different." I was really pumped that I wrote this!