I compete in so-called "combat" style rifle and pistol matches. They are run by outfits whose acronyms are IPSC and IDPA, and are truly a "blast". (Google for their homepages, get in touch with your local clubs). Asking around at gun shows, gunshops and shooting ranges will quickly put you in touch with the right people, as will posting on sites like "thehighroad.org", AR-15.com, etc.
I also compete in karate tournaments, altho I am getting too old for the "no-contact" stuff. It's too hard on the knees and elbows, to be "pulling' my blows and kicks all the time. With full protective gear on both men, tho, you can let it (nearly) all hang out and learn a lot about what works and why.