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.
During setup, after mulligans, you have the option to place Basic Pokémon onto your Bench before either player gets a turn. The question is, should you do so?
If you are going first, the answer is no. You can always see what your opponent is playing before committing anything to your Bench. There is nothing like Absol Prime in the format to punish you for benching Basics during your first turn instead of during setup.
If you are going second, the answer is still no... most of the time. Why?
If your starting Pokémon is played in a variety of decks and you don't bench (and hence reveal) anything else during setup, it keeps your opponent guessing what deck you're on.
Iron Bundle. If you're going second, put your ideal starter in the Active Spot, and bench something else during setup, your opponent can play Iron Bundle and use its Ability on their first turn to force out your ideal starter.
Prime Catcher. It has a disruptive effect like Iron Bundle, yes, but in addition, if your opponent desperately needs to use Prime Catcher as a switch card on T1 for some reason, they can only do so if you've given them a target for it (i.e. if you've benched something during setup).
However, there is one reason you'd want to bench something during setup going second, and that's avoiding donks. The most common kind comes from decks that will go first and assemble Pecharunt + Brute Bonnet + Ancient Booster Energy Capsule + Perilous Jungle, KOing your starter if it has 80 HP or less. If your starter has low (30-40) HP, a couple of Iron Valiant ex's and switches can also do the job.
That said, donk decks are not that common, so if you have to lean towards one side, it'd be the side of not benching during setup. Nevertheless, if you don't know what your opponent is playing but don't want to take any risks, there are ways to cover both Pecharunt donks and Iron Bundle/Prime Catcher disruption at the same time:
If your starting Pokémon can survive Poison (e.g. it's a high-HP ex, or a Darkness-type (and hence immune to Perilous Jungle) with 70 HP or more), you do not need to bench anything during setup.
You can bench a duplicate of your starting Pokémon, or a Pokémon that retreats for free (e.g. Mew ex, Latias ex), or anything at all when you have a switch/free retreat card in hand that you're prepared to use.