I was an active member of Smogon's in-game tiers subforum for a little while. Here are a few things I learned from them.
It's not about how powerful your team is at any level, it's about how powerful your team is with any amount of experience. Experience is usually the most valuable resource in the game, and your Pokemon's levels depend on how you spend it. The biggest consequence is that smaller teams are better than bigger teams. If you have enough experience to raise 6 Pokemon to level 50, the same amount of experience can raise 4 Pokemon to level 57 or 2 Pokemon to level 72. Additionally, Pokemon that arrive at an unusually high level (like Emerald Rayquaza or HGSS Magikarp) or gain boosted experience are more likely to be useful, and Pokemon that hatch from eggs (or arrive at an unusually low level) are almost never worth using.
It's not about how easily you can win battles, it's about how quickly you can win them. I didn't say time is a valuable resource in the game because it's valuable in real life. If you disagree, feel free to catch 6 random Pokemon and level grind them to level 100. Knocking out opponents in less turns also means you're less likely to deal with annoying moves like thunder wave or double team. Pokemon that are easy to get, like the starters, are usually better than Pokemon that take a long time to get, like DPPt Milotic. Pokemon that have a high attack stat and a powerful STAB move are often worth using. Of course other things, like evolving early, other good stats, good typing, or good coverage or status moves help too, but attack stats and STAB move base power are usually the most important factors.
It's not about preparing for the Pokemon League, it's about playing well throughout the whole game. The best Pokemon are often the ones that you get early and evolve or learn better moves frequently enough to stay useful. (note that evolution is necessary for Pokemon that start with low stats, not for Pokemon like USUM Hawlucha) Pokemon that you get later and are useful for the rest of the game (like RBY Jynx) are sometimes also good, partly because leaving a slot empty for half of the game means your other Pokemon get more experience. Pokemon that have absolutely destroy 2 early-game boss battles but have bad stats or don't learn good moves afterward are often not useful. Similarly, Pokemon that need a high level, high friendship value, or rare item to evolve are also often not useful.
When your Pokemon knows only physical or only special attacks, you can (usually) determine which one will do the most (average) damage by calculating base power * accuracy * STAB * type effectiveness for each attack. Of course there are edge cases (mixed attackers, moves with variable power or damage, moves with drawbacks, held items, abilities, etc), but multiplying these 4 numbers should get you through more than a majority of battles.
The best status moves are usually accurate sleep moves (like yawn, sleep powder, or lovely kiss) or attack-raising moves (like swords dance or calm mind). Many bosses will use a weak Pokmon that just lets your Pokemon set up. If the AI is stupid enough, even +1 moves like howl or work up can be useful.
If you want more advice about which attack moves or status moves are useful, Fizz's post is pretty good.
If you like items but don't like talking to everyone, each time you reach a new city you can look up all of its items on Bulbapedia.
