A lot of people worry about hypermobility, and while it's important to be aware of, there's no reason why you can't be out there training. :)
For anyone who is hypermobile and looking for a place to start, we recommend Elements. Although it doesn't directly address issues like hypermobility, it's fantastic for strengthening and mobilising your body, and would be especially good for your joints. We have clients with hypermobility go through this program with a lot of success. What we usually suggest is that you keep sets, reps, and time, low to begin with, and you approach new movements slowly and with care.
The most important thing with Elements is the stress we place on high quality, fluid movements over quantity or intensity. If a movement is painful or causes discomfort, there's no need to push the range of motion or level of difficulty. It works for all levels of physical ability, and we can help with any adjustments that might be needed.