If you win the opening coin flip, you get to choose whether you go first or second. The player who goes first cannot attack or play Supporters on their first turn. Some decks prefer going first, whereas others prefer going second. Below are the factors that would push a deck towards one option or the other:
You want to attack with an Evolved Pokémon as soon as possible. While you can attack on your first turn if you choose to go second, if you need to attack with an Evolved Pokémon, the Evolution will be the bottleneck. The earliest you can evolve is on your T2, so if you go second, your opponent gets two turns to try to disrupt you (opp T1, your T1, opp T2, your T2), but if you go first, your opponent only gets one turn (your T1, opp T1, your T2).
You want to attack with an Energy-hungry attacker and KO your opponent's weak Basic Pokémon before they evolve. Imagine something like Wellspring Mask Ogerpon ex or Iron Hands ex; their attacks cost 3-4 Energy, so you need a turn to charge them up, and you're only attacking with them on your T2 earliest. Your opponent's counterplay is to evolve their Basics out of KO range, which also happens on their T2 earliest (they can Technical Machine: Evolution their Benched Pokémon, but if the Stage 1 isn't an ex, it's likely still within KO range of your attacker.) The winner of this race is whoever gets their T2 first, which will be you as long as you go first (your T1, opp T1, your T2, opp T2).
You are playing a deck with the Noctowl engine. Same logic as attacking with an Evolved Pokémon; if you go first, your opponent only gets one turn to try to disrupt you. You might think that going second should increase your consistency at finding Noctowl, since you would be able to use a Supporter on your first turn, but if you take a closer look at how Noctowl decks are built, they don't have many Supporters that can help draw into or search for Fan Rotom; typically just 1 Iono and that's it. The main way you find Fan Rotom is with Items (Buddy-Buddy Poffin, Nest Ball, Ultra Ball), which can be used on your first turn regardless of whether you go first or second. So the increase in consistency from choosing to go second is not great, and you're better off going first.
You are playing a deck with Carmine. The whole point of putting Carmine in your deck in the first place is to use Carmine on T1 going first — if that weren't the case, you would use a different Supporter lineup, like 4 Iono instead of 4 Carmine — so when you're blessed with the option of choosing to go first or second, you're going to choose first.
You want to attack with a Basic Pokémon as soon as possible. Some common examples are Budew, Cleffa, Technical Machine: Evolution, and Technical Machine: Turbo Energize.
You want to deny your opponent from attacking on their first turn. Same logic as the previous point. If your opponent has Budew or Frillish, you'd want to go second so you can dump all the Items that your first Supporter finds before they Item lock you.
Note that your opponent will always be able to Item lock you before you can play Rare Candy, whether you go first or second, because Rare Candy can only be played on your T2 earliest. If you go first, the turn order is your T1, opp T1, your T2. If you go second, the turn order is opp T1, your T1, opp T2, your T2. (The underlined turns are when your opponent can attack with Budew or Frillish; note that they always occur before your T2.)
You want to play a Supporter as soon as possible. You can usually tell by looking at the deck's Supporter count, sans the Supporters that aren't useful on T1 (e.g. Boss's Orders, Professor Turo's Scenario, Briar) — if the deck has 9 or more of these, that points towards it wanting to go second.
If your deck plays the Arven for Buddy-Buddy Poffin + Technical Machine: Evolution combo, that's a sure sign that it wants to go second, since that line demands both a Supporter use AND an attack.
Sometimes you may want to choose your less-preferred starting position in order to deny your opponent their preferred option (going second to deny an Item-locking attack is an example that's already been mentioned). If you lose the flip and your opponent doesn't give you your preferred start, you should look out for ways to play into the strengths of the position that you've been dumped into. Of course, whether you have the means to do so will depend on what you draw, so sometimes you won't have the resources to make it happen, but the main thing is to be able to recognize the opportunity when it arises.
For example, if you're playing a Noctowl deck that usually wants to go first, but your opponent makes you go second, you can try to attack with Fan Rotom on turn 1 and get an early KO. Another example is if you're playing a Stage 2 deck that usually wants to go second, but your opponent makes you go first; you can try to assemble Rare Candy + Stage 2 attacker by turn 2 and overrun them with this aggressive start.