Girls that start at three stars are very difficult to star up further. Those that start at one star let you regularly gain a few shards from normal or friend gacha. Additionally, the girls available in the league, competition, and trial shops don't change, so if you focus on one of them (or rather, one for each shop), that's what you can reliably star up to higher levels. You'll generally get league shop points much faster than either of the others, and competition shop points faster than trial shop.