I have been researching several martial arts facilities in my area. I am looking for something that will help me in real life situations, become more disciplined mentally and psychologically, get into shape, and to be a tool for de-stressing after a hard day's work. I’m a 43-year-old man and weigh approximately 310. I do have some arthritis in both knees, but not to the point where I can’t walk. I’m not really interested in kicking a banana tree in half, picking a fight with a brick wall, or tearing wood planks apart with my hands. Only in part because I don’t see any real reason why breaking a brick with my head helps me find inner zen. I have read about Jeet Kune Do, Vovinam Viet Vo Dao, and several others. Any advice on which one or ones would be a great start? Oh, btw, I have never had any martial arts training and can’t jump kick to save my life.
Well, I personally think that any single martial art cannot fulfill all your specific needs.
I am looking for something that will help me in real life situations
For real life self-defence, I would recommend Krav Maga. It teaches you the best ways to avoid a fight all-together, neutralize your attacker and flee the scene, or as a last resort, use deadly striking and grappling to finish your opponent. This is not as taxing on the body (knees, wrists, lower back) as is Boxing or Muay Thai. If you want to be really really good in grappling (submissions, arms/legs/head locks, chokes etc,), then go to a gym that has a separate jujitsu class (not those that teach mma, everything in one class).
...become more disciplined mentally and psychologically
Any martial art at a good gym will help you with discipline. If the trainer is anything like the head master of Cobra Kai from the movie Karate Kid, then it won't matter what martial art you choose, it will not fulfill your desire to become "disciplined mentally and psychologically". So pick your gym wisely. Look at the people who go there. Are there people in the gym who is close to your age? Talk to them. How do they feel? You will also need a trainer who you will admire and respect.
...helps me find and inner zen
I suppose others can explain this better. I feel that modern MMA gyms lack that Ying & Yang concept of martial arts. Given you are new to it, the striking (hitting the bags, sparring, pad work) can be a bit overwhelming at first. Also, most people in the gym will be talking about martial arts which can be daunting for beginners. If you want zen I would suggest don't go for boxing. Karate, Kung Fu, Taekwondo are all great arts with both the fighting part as well as the spiritual part. Muay thai too but only if you are in Thailand. If you don't find those, you can take up a beginners kickboxing class with yoga on the side for mental and spiritual relaxation.