Don't choose an art, choose a school.
I'm suffering from arthritis in my knees and medial epicondlyitis (a temporary condition in my elbow which gives me some understanding of your plight). I practice Tai chi and Aikido; the style of aikido I practice (Tomiki) borrows heavily from Judo. My sister was an Olympic level Kareteka until she injured her elbow; she switched schools because her senior teacher wouldn't permit her to adapt her training to the injury.
Make sure the school respects injuries. My primary school is probably all over 30, and most of us are over 50. Injuries happen, and if we want to keep training with one another we have to learn to respect those injuries. We've dismissed students for failing to respect injuries. Look for a school with older students, and teachers who are used to teaching older students.
Many schools will use tape (duct tape or red tape) to indicate an injury; training partners should ask about the tape if the joint is involved in the technique you're practicing.
Adapt your training. Because my elbow is munged up, I've been practicing all the techniques on the reverse side - Some of the techniques get more complicated in reverse, but my training partners have been enthusiastic about using the complexity as a way to test our understanding. (all techniques should be practiced on both sides as a normal event, but we happen to be working on a kata which is asymmetrical for reasons that are not really relevant to your question).
Tap out. Protect that joint. When the technique puts any pressure on my joint I tap out before there is a problem. At the moment I have a glass elbow. If there is any doubt as to whether the technique is effective, we switch sides and do it on my stronger elbow. My job as Uke is not to test my partner's effectiveness, it is to react correctly, and tapping out fast is reacting correctly. That is a general rule; there are exceptions, but they can be accomodated
Don't do the dangerous stuff. There are techniques I can no longer do because the arthritis in my knees make me weaker in certain postures. When we do kneeling work, I either bow out, or do the technique standing up. My temporary injury to my elbow makes push hands dangerous, so I've had to take six weeks off. I still perform and practice Tai Chi, but push hands is the wrong thing for me right now. Might not be a problem for you under the conditions you describe. There are other techniques that I refuse to do because if my knee were to give out, there are situations where it might injure my partner. (my knee folded during shihonage once and nearly separated my partner's shoulder. I do shihonage differently now).
Get a second medical opinion. I say this for two reasons:
- Most of the aikdoka I work with share an orthopod - because he used to be one of us, and he knows exactly what locks are dangerous. Different doctors have different levels of familiarity with martial arts. An adequate answer from a GP is adequate, but a second opinion from a doctor/martial artist might open whole new worlds of possibility
- Most chronic injuries can be partially compensated through some form of physical therapy. I can compensate for my elbow by strengthening the muscles and relying less on the damaged tendons. I can compensate for the knee by making sure that the muscles are strong enough to bear additional strain. Check with the doctor to see if you can design a program of stretches and exercises that will maximize your participation and minimize the chance that you'll exacerbate an injury.
The most important tip I'll give you
For Tomiki Aikido, the promotion to second degree black belt involves a set of kneeling techniques. I can't do kneeling techniques, and when I try, the effort is embarassing to all concerned. Sensei allowed me to test standing up. The standing techniques teach an entirely different set of lessons, and if I ever reach a teaching rank, I'm going to have to confront that gap in my trainng. But Sensei was willing to work with me to create a demonstration that allowed me to show my mastery of the portion of the art I can show. If the teacher you're working with won't adapt the technique to your limitations, leave. There is no excuse for that. Working through a chronic injury with the risk of doing further harm to your body is bad art, bad martial, bad personal development, bad budo, bad human relations. Failing to adapt to the student is contemptible.
On the flip side, I need to accept that I'll never be the lineage master, and that if/when I teach, I need to address that so that I don't shortchange my students.
Some people will challenge me because they believe that the art isn't pure if it is adapted. With all due respect, that's crap. My teacher's teacher believes that, and although he is a brilliant man, on this count he is wrong. The art is going to be different for a 5' 100lb girl than it is for a 6'1 300 pound man. Different for people with long arms than short arms. Shuhari. But that whole rant is the answer to a different question so I'll shut up now.
** Ask** the teacher how the two of you could work together to achieve your goals. You have realistic goals specified in your question, and any decent teacher should be able to accomodate your limitations.
You should be able to do what you want to do. I do joint locks, I do throws, I do the occasional high flying breakfall (flying breakfalls are actually easier on my knees than low soft breakfalls; but Sensei doesn't like me to do them because he wants me to come back.) Find a school where you can achieve your goals.