Any open source wallet will allow you set your own fees, so there is no cheapest. You can pay 0% if you wish, it is just that the miners will likely never confirm it and as a result other Bitcoin nodes won't even relay your transaction if it is bellow certain amount.
Electrum is a popular light weight open source wallet and Bitcoin Core is a backbone of the entire network which stores, validates and replays all transaction on the network.
I think the OP did not express himself clearly. He does not talk about the transaction fees for sending bitcoins but those related to trading (buying/selling)
@gtinvest it doesn't matter if you trade small or big amount because the fees are (usually) based on a percentage, as mentioned by OmegaStarScream. On average the fees are more or less the same, about 0.25%