I couldnt find anything in the rulebook that tells how to handle the determination of the starting player respectively the player order: So we assumed that the "starting player" is chosen randomly the very first turn, after everyone refreshes he resolves all his actions, then clockwise all players resolve their actions, afterwards discard/draw/event/draw. The next turn the player clockwise following him becomes "starting player" and everything repeats etc.

Did we play it right?

That gives the starting player the advantage to buy neutral cards first and to engage (event )enemies that have been revealed during the last turn first...

I played it like that at first, but I was taught. After getting the game and reading the rules, I could not find anything that said the 1st player token moves on. I believe the 1st player stays 1st player. The advantage of going 1st is offset by some events hurting the 1st player more. Choosing 1st player randomly seems logical. This may all get covered in the FAQs. Cheers!

Rulebook Page 4

Setup

4. Determine Play Order: The youngest player goes first. Play then proceeds clockwise.

It doesn't mention anything in the rules about switching player 1. It does state to place the event deck in between the first and last player. If you were to shift the event deck each round it would give more time in between events and unbalance the game. As well as previously mentioned there are cards that harm the first player and benefit the last player to make up for the imbalance of getting first chance at the event monsters.

On a side note it wouldn't always need to be the youngest player going first, but this was also probably done to balance out the skill levels.