If you have $1000 to spend ... do you have any bike repair experience? Nothing is less fun than waiting for parts to arrive, or realizing you need a tool or part which you don't have.

If you are confident with your mechanicking skills, and not worried about losing riding time to repair time ... then you can get some amazing used bikes for $1000.

The key to buying used online is patience. Look for bikes only a couple years old ... often people will buy really expensive bikes, thinking they will start riding, and a year or two later sell them for 2/3 off because they never took them out of the garage.

I have some experience with the benefit of regular exercise, and cycling is a great way to get out of the house and exert oneself. I would also suggest tai chi, qigong, or yoga as both a stretching/relaxing practice, to get some activity on non-riding days, and because it helped me when I needed it.