I'm all for calorie counting, because I believe it's the best way to lose weight without going wacko trying to eliminate particular foods. I don't eliminate anything -- I just stick to a certain calorie level, and that seems to be the only kind of structure I can stand. If that's not enough structure for you, you might be able to find a planned diet that incorporates the right number of calories for you or you can add some healthy foods to an established diet if you need more calories.
I think we definitely tend to underestimate our calorie counts unless we're really really careful about measuring and counting everything, so you may be eating more calories than you'd think on a regular day, and the 2200 might actually work for you. Or you could start with 2000 and see what happens after a few weeks. Right now I'm trying to stay under 1800 and when I stick to that I lose 1-2 pounds a week, sometimes more.
As for eating more on days you exercise, that just depends on how your body feels, I think. If you're doing moderate exercise and not doing anything terribly strenuous, you may want to just keep your calorie level the same. I just think of exercise as a boost to the calorie burning and I don't generally like to add those calories back. The only times I've needed to eat more were when I was in much better shape and was doing very long runs (I'm talking 10 miles or more here). I simply needed more fuel then. If you're doing a bit of walking and you have enough energy to do it, then I'd say don't eat more.
Good luck with whatever plan you decide on!