Accessing the Pi from your computer

There are actually several ways you can access the Pi from an external computer: Wifi, ethernet over Bluetooth or serial, and serial terminal.

With the Pi Zero W, wifi and bluetooth are built in and wifi would be preferred; with the plain Pi Zero the serial line is the only option (unless you add a Wifi dongle which probably also means adding a small USB hub)

Setting up PPP or some other internet protocol over the serial port and running it at max speed is probably the best bet for a good user experience, though it would take a bit of setting up. Using the serial port as a terminal is by far the simplest but then you have to transfer files using kermit or shut down your Pi to remove the SD card so you can write to it (or use a small USB hub to attach a card reader for a second card, but if you're doing that you might as well use a Wifi dongle and forget about serial terminals)

The hardware for a serial terminal or a PPP connection is quite simple and cheap:

Serial to USB adapter