I don't think there is a right or wrong number of balls to bring to league. There are times when I bring my 4-ball roller with the Joey Strap, so I end up with 5 balls. I obviously don't need that many since my house shot is fairly consistent week to week. Still, I like having options, and sometimes it's just fun to pull something different out of the bag from time to time. If I wanted to, I could easily get through a league set with one ball. Still, I don't often do that. Again, I like having different options at my disposal.
Now, as to recommendations, I think two balls would be sufficient for most people, three if you want a dedicated spare ball. Have one for medium to medium-heavy, one for medium to medium-light, and, again, a spare ball if you feel the need. Most house shots are so ingrained that they make different balls react similarly on the lane anyway. Get yourself two entry-level pieces that cover the aforementioned conditions, and you're probably more than good to go on your THS.