If what you want is weight loss, you don't need to overcomplicate things—all you need is to eat fewer calories, and if you want to do exercise, do cardio. Sounds like the elliptical is going to be your friend.
Muscle building is great, but I say this as someone who enjoys bodybuilding: If you try to build muscle at the same time as you lose weight, you're going to be so hungry that it's going to impede your efforts to eat less. I'm all for folks doing strength training once they're not as invested in fat loss, though.
Good luck!!