It depends on the token you want to swap because not all token run in all chain, if you're looking for cheapest network, just pick the unknown one lol. The emptier the network, the cheaper the network.
agreed with the statement, also fee depends on the scalability of the blockchain as well.
blockchain like solana is so crowded yet fee still minimum compared to ETH.
but one thing that OP need to watch out, be sure to set slippage tolerance at minimum as it can be if you are using L2 with relatively low tx which equates to lower fee.
personally I just don't bother I just go to the most crowded L2 just for the sake of liquidity.
because imagine you are paying low fee yet the slippage is 5%, you literally lost the 5%.