because most of the nodes will reject including anything lower than 1 sat/byte into their mempool, if I remember correctly.
Just a small correction:
The minimum fee you have to pay for a transaction is 1 sat/vbyte not 1 sat/byte.
A transaction with segwit input(s) can be broadcast even with less than 1 sat/byte.
To OP:As every block has a capacity of 1 vMB and miners can't include any number of transactions in a block, they prioritize transactions based on their fee rate per vbyte to maximize their profit.
So, as already stated, the higher fee rate your transaction has, the more quickly it will be confirmed.
The fee rate you need to set for a transaction depends on how fast your transaction want to be confirmed and the network state.