I started my fitness journey years ago with pushups and situps at home. It can be a great way to get fitter! (These days, though, home workouts are my backup plan. Say it with me: three is two, two is one, one is none.)
Rowing exercises with tension bands can strengthen accessory muscles in the back. This may make the neck harder to injure, but I'd recommend getting the okay from a physician before working too much on a sore neck. In any case, it's definitely how I keep sitting at a desk from murdering my posture.
Though I don't own this particular brand, these look to be well-made. I like bands where the end of the band doesn't directly attach to the handle, but instead attaches to a nylon mounting for a clip. This minimizes the risk of breakage.