I was thinking about accepting Tether as a payment currency. But that would make it more complicated for me since in that case I would need to have wallets on all different blockchains. Also sender needs to know to which wallet to send the coins
I'm right about this?
It actually depends on you whether on which chain will you accept the payment. You can simply accept it only on ERC20 as an example, and then you can state you only accept it on the Ethereum chain to the sender(s).
If I might ask, do you already have some payment processor or do you want to receive the payment manually?