A team with a successful running attack is a team that controls the line of scrimmage and the tempo of the game. It is usually a team whose offense has the ball more than the opposition's offense does during any given game. The next time you see a game on TV, watch a play or two. Take note of the running plays. The side that can push the other around usually wins.
Fullbacks usually go a bit bigger since their primary function is to block.
They are the most likely targets for the quarterback when the team calls a passing play. While running backs function as pass receivers as well, a team will not prosper in its passing game if it doesn't have one or two top flight receivers on its roster. There are actually two kinds of pass receivers, the wide receivers, and a tight end. As with running backs, there can be many combinations, but the most common combo is the two wide receiver one tight end set. He's usually a lot bigger than his wide receiver counterparts.