As Kuri says:
A Brazilian Jiu-jitsu/wrestling/judo for grappling, thai boxing/kickboxing/karate/boxing - or any combinations of the above.
Why not do all them at once? Well you can if you learn Vale Tudo! (portuguese for ‘anything goes’, modern mixed martial art style)
If you can’t find a Vale Tudo club then I’d choose Thai-boxing and Brazillian Ju-Jutsu. That way you’ll have stand-up and ground skills.
You generally won’t find rubbish teachers in MMA orientated martial arts as these guys have to prove themselves in combat and they get quickly found out. You also don’t get power trippers (like the cobra karate sensei in karate kid) cause these guys have nothing to prove to anyone, they have earned respect the hard way.
You don’t get the spiritual side but if you want that I suggest doing it properly and taking up Buddhism. But you will get a sense of confidence and well-being with your ‘proven’ new found skills. These guys (with a few exceptions) are not thugs or bullies and have immense self-discipline. They don’t need to beat up on weaker individuals cause they can but like to prove their skills against an opponent of equal worth.
You don’t have to look at competing either. Just use it for self-defense and just to enjoy the learning experience.