What types of exercises should I do? So far I’ve been doing push-ups, situps, and jumping jacks, and using an exercise bike in the afternoon. Are these good? Should I do more?

That sounds like a good workout. If you feel like it’s too easy though maybe you some more lower body and core or weight training. One thing I would recommend is doing crunches instead of sit ups. It gives you the same intensity and is much gentler on you neck and back.