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Depends. I replay the games over and over, so I have a number of approaches.
If it's my first play-through then I usually use the starter up until I find something better. On replays I almost always box the starter. I almost never use gift pokemon or legends.
Sometimes I'll go on a team planning site and plan out my team very carefully, sometimes I just catch whatever I feel like using, regardless of if it makes for a balanaced team, sometimes I go for a certain theme (all food-based pokemon, all cat pokemon, etc.), and sometimes I just make a concerted effort to use mons that I've never used before.