We could give you some good links if you narrowed down what sport you were interested in. IDPA, IPSC etc have web sites that list local clubs, contact numbers etc.
Let me say this. No matter what sport you decide to try, it will make you better. There is nothing like having every shot counted that will give you the incentive to make every shot count. Once you try it, you will see how and what to practice. And you will practice with a clear cut goal in mind and a way to measure your progress. Don't worry for a moment that you need to reach a certain level before you can start competing. If you have the concept of safe gun handling, you are ready.
You know the rest. In the books you have read
How the British Regulars fired and fled,
How the farmers gave them ball for ball,
From behind each fence and farmyard wall,
Chasing the redcoats down the lane,
Then crossing the fields to emerge again
Under the trees at the turn of the road,
And only pausing to fire and load.