How shall I fast and reliably transfer 300G files from a computer to another?

I want to transfer ~300G files from a laptop to other in the same local wifi network, for back up purpose. (I am running out of the space of my only external hard drive, and can't afford anything. Someone was kind enough to leave an old laptop in a dumpster for me to uncover.) Both now run Lubuntu. What is the fastest and reliable way to transfer the files? By rsync, scp, or some other commands? Could you also give some concrete commands to transfer for example two directories (and the files under them)? How is the transfer speed of the command you will use compared to using an external hard drive to physcially connect in turn to the computers via a USB cable and perform the transfer indirectly, If there is another external hard drive available in a dumpster in the future ? Thanks.