-I usually don't pre-plan my team before playing a new game, or replaying it later down the line; I'll just catch and use Pokemon that I like or would be cool to try out. Usually I try to have a full team by the 4th-5th gyms in their respective games since I don't particularly like catching Pokemon super-late in the game. There have been exceptions, such as me pre-planning my team before playing White for the first time, or cutting through parts of the game to catch a Pokemon (such as Remoraid from Gold), while skipping possible trainers until when I "naturally" reach that route. I also do try to have a Grass, Fire, and Water member on my team when possible. Also, if I encounter a shiny Pokemon while playing through the story, I always add it to my team.
-Adding on to my first point, I don't usually favor certain starter Pokemon types; I just pick starters I think would be cool to use. If I'm replaying a game, I will usually pick a starter I haven't used before or haven't used as much however, unless it's a starter that I
really like.
-I don't dedicate team members as HM slaves; I catch a full party of Pokemon that all battle evenly, and distribute HMs evenly among them. Once I reach the Pokemon League, I'll fly to the move deleter, delete the HM moves (except the good ones like Surf), and teach better moves to them for the Elite 4 gauntlet.
-I avoid trading until post-game, unless it's to evolve a trade-evolution Pokemon like Kadabra.
-Mirroring what
Kurona said, I always try to keep my Pokemon's levels even. If one of my Pokemon hits lv 40, for example, I'll switch him out and let other members battle until the whole party hits lv 40.
-I never use my Master Ball in-game. I don't bother battling/catching legendaries until post-game unless you are forced to during the story (which I really hate btw). If I have to catch them to advance the story, I catch them the old-fashioned way of lowering their HP, inflicting status, and chucking as many Ultra/Dusk/whatever balls as possible until it's caught.
-I always keep the Pokemon I use in my in-game team, as well as any random shinies I catch. If, by some RNG miracle, they have good IV's & Nature, then I'll even wipe and properly train EVs to them and use them post-game in battle facilities such as the Maison.
-When I buy a new game and beat it for the first time, I never restart it; instead it becomes my main game for things such as WiFi trading/battling, and storing Pokemon. I usually will buy the opposite version later on for casual plays, that I can restart whenever I want.
-I'm the minority here, but I actually never do nuzlocke runs. To me, nuzlockes go against the very nature of the game, and there are better ways to increase difficulty in a Pokemon game (use lesser-used Pokemon, no Exp Share, minimize grinding, etc.). If I really want to play a game where permadeath is possible and resources are limited, I'd rather just play a Fire Emblem game.