Game Help: I don't think I'm playing the right way...

Let me ask you a question:
How do you choose your team? Do you use the Pokémon you like simply because you like them? Or do you go for the strong ones, the kind of Pokémon you would see on competitive play?

Lately I've been thinking about the way I choose my Pokémon. Recently I finished Pokémon Pearl with a premade team, and it was pretty easy. Weeks after that, I found my old GBA SP, so I took the opportunity to finally beat Wallace. And to me, it looked like the team from that game was made by other person.
I mean, sure, you may argue that the savefile is old so my team is not as good as it could be if I played the game now, but then again, my Pokémon Moon team is not much better.

Right now I'm playing through Black and Ultra Moon, with 3 badges on the former and no trials completed on the latter. I was considering beating both games with premade teams again, but what's the point?
And then I came to the realization that I don't know how to make teams.

So here's the question: What are the things I've got to consider when making a team? How do you guys and gals choose your Pokémon?

Thanks in advance.

My teams are somewhat predetermined. I might think of Tauros or another random pokemon and suddenly be in the mood to use it, so I save room for it later on. Or I'll need something to use an HM so I start thinking of stuff to catch that can learn the certain move.

I try my best to get type coverage, so I start narrowing down whats available. I pretty much figure my team out as I go along, but I might have a couple I already want to use before starting the file.

There is no right or way to play Pokemon. Just have fun. It may seem cheesy, but its true. Personally I just choose the Pokemon I like whether they are strong or not. After all, I want to play the game with the Pokemon I love the most by my side.

I usually have my favorites (Deerling/Sawsbuck, Skitty/Delcatty, Absol, Sharpedo) and then whatever else I find cool

Basically the big thing when forming a team in the games is to be able to comfortably handle the types of the gyms/trials and E4, and in pre-Gen 7 games, have all the necessary HMs on hand.

There's usually enough shit to pick from that you can mostly roll with whatever you feel like while doing the above.

Like noa said, theres no certain way one should play Pokemon. If you want a planned team with good type coverage and balanced roles than go for it. I usually pick one old favorite in a playthrough and the rest are from whatever gen Im playing in, I try to keep my team balanced too.

The right way to play is to not worry about minor stuff like team comp and type synergy. Almost literally every Pokemon you can encounter can be used effectively; my latest E4 run on Emerald featured an Illumise with no attacking moves as the MVP. (charm/moonlight/toxic/light screen) As long as you understand what each Pokemon's strengths and weaknesses are in different roles, there's no need to worry about min-maxing.

First time I play a game I go for all the pokemon of that gen. No older gen pokemon at all. Sometimes if I play through again I'll cheat a little bit and breed 6 pokemon with perfect IVs that I plan on using competitively. Then other times I'll goof around and use Aipom or Farfetch'd or guys I know kind of stink to use in battle, but surround then with powerful pokemon. It changes every time.

I usually pick up my team along the way, although it mostly consists of pokemon I like I try it to be balanced it terms of type coverage. I usually also try to have 3 physical attackers and 3 special attackers and if possible one of them being really bulky tank.

Also I try to avoid using same pokemon all the time, simply because it gets boring. There are so many pokemon to choose from after all. :)

My general policy is to never use two Pokemon of the same type and thus share the same weaknesses, because it just puts a strain on the other members. As for the way I construct my team, what I usually do is check the encounters on each route, and go through them based on their ability, moveset and stats, and decide which one would benefit me the best in the long run. If there's no Pokemon on the route that fit my criteria, then I don't really take them on and just move on through the route, eager to find more creatures.

Also, despite them showing them to us, I never take Pokemon that you'd find endgame, because they'd usually have quite a lot of catching-up to do with my other teammates.

For my in-game team, I honestly just use whichever pokemon I like the best. I have a weird rule that I follow though: For the first time playing through the game, I only use pokemon introduced in the generation. So for XY, I only used new Kalos pokemon; for ORAS, I only used Hoenn introduced pokemon, etc. For SuMo, I counted Alola forms as new pokemon.

I find that doing it that way helps me keep from always using the same four pokemon over and over again, and lets me get familiar with a new generation. It's also easier to build a team that works well together when you've got fewer possibilities to worry about. (I usually wind up using a four-mon team that's overleveled as all get out. It's a relic from the HM slave days.)

I have always one or two HM Slaves and after I choose Pokemon who I think look strong and cool. My only rule is having type diversity and having every weakness covered with all 16/20 moves I can use.