MMA is awesomely fun and not as dangerous as you may think. I train 2-3 times a week and while I am too old for competition myself, it is great fun to help the younger students prepare. You get both a physical and mental workout everytime you step on the mat. Every move has counters and you have to think several moves ahead to get yourself into a superior position. If your opponent is younger they will probably be faster but you have that big brain going for you. You can create a better defense and win the positional battle. Pretty soon your opponent is tired and in a bad position and you counter-attack for the win. I have beaten opponents much bigger, faster, and stronger than myself and lost to your typical "98 lb weaklings". You will learn a lot about anatomy, physiology, psychology, physics, and much more.
As far as health benefits go; I lost 50lbs in my first year of training (and gained a lot of muscle), I am totally off my blood pressure medication, and I am about to go off my chloresterol medication. I am more focused which leads to me being able to evaluate situations and react to them faster at work (it makes you a better geek too). If you find yourself a good gym with a trainer that really cares about their students then they will ease you in at a pace that will be challenging, but not dangerous. When I started I would be gassed after a 15 minute warmup. Now I do back to back striking and ground fighting classes and still can stay after and help out new students.
I would highly reccomend you try a free lesson and see what you think. You might just be able to improve your health and your mind at the same time. Just remember in practice you are there to learn techniques and counters not to hurt each other. Take care of your partner and tap fast, if you want to prove how tough you are there is always competition. You do not take many head blows and if anything solid connects (either a strike or a throw) then you are required (at least at my gym) to sit out the rest of the lesson and have a trainer evaluate you to see if you need futher medical help. If
this guy can do it, then so can you. The first lesson will leave you sore and tired, but it gets better, after a month you will be looking forward to training sessions and plotting how to take down the guy that submitted you last week.