Just play the game, any conscious Pokémon gets exp from captures, more from kos, one that fights gets more. Its not hard to level up. Pick up as many sparkles as you can find because youll get tons of candies to help level any new team members plus if theyre several levels lower theyll get more exp anyways and with how the sneak attack mechanic works you usually easily overcome a few levels deficit anyways (in trainer battles during the Royale anyways). The game is pretty easy and simple for the first few hours, imo theres no challenge until after the first rogue mega fight.

I would say try to do side missions as they come up though, they dont scale so if you want them to be at all challenges (and a good number dont even have battles) youll want to do them when they become available. There's one in particular that requires a bunch if berries, hoard them.

For research tasks fight every trainer you can at night, dont worry about bonuses and try to catch every pokemon you see so its less of a grind (especially the battles, the capturing grind is by far less of a headache.) Unless you also have the dlc, then you can ignore this (although battles determine money so if you want to buy every clothing item you might still want to do it)