Look at the National Field Archery site.
http://www.nfaa-archery.org/
That will get you started. There are various kinds of both outdoor target shooting and indoor. Don't know where you live. Seems to vary in popularity by region. The sitehas links to state organizations that should hopefullyhook you up in your local area.
Also use the dealer locators of the various bow companies tofind yourarea archeryshops. Even if they don't have shoots themselves, they or their customers will know what your locale has to offer.
55Lbs is plenty for indoor target. In fact guys often go lighter poundagefor indoor since you are typically shooting 45 or 60 arrowsin a short time, depending on what type of shoot it is. To get really good accuracy you want a bow you can draw easily and stay consistant with.