In my experience, the stinging pain goes away after a few seconds. Of course, the closer you are to the muzzle of the gun, the higher the velocity of the pellet when it hits you. Thus, more pain may be experienced when shot at close range rather than farther away. In general, a paintball impact will leave you with a light bruise, but your most annoying injuries are more likely to be scrapes and scratches from the local terrain. Almost all paintball 'fields' rent equipment and welcome new players.
Most commercial fields allow walk-on games, where anybody can show up and play.
You don't have to have an organized team or go to an organized field in order to play, but it simplifies matters for beginners. For the first few games you should play on a well organized field. Size is not the best way to judge the field. The things to watch for are the number of referees on the field for each game and the explanation of the rules. There should also be a sufficient number of referees for the number of players, one referee can not handle a field with fifty people on it.