The Zero is just a stripped down Pi1 series (ARMv6). It can do anything the Pi A/B/A+/B+ can do, but it may require some additional accessories due to its lack of a USB+Ethernet hub on-board (oh, and no analog audio either). And it doesn't have the "Display" connector as well, so you'll need a screen that uses HDMI or the GPIO header.
For a GPIO screen (HAT), you can solder on a header and plug it in like any other Pi. The latest version of Raspbian supports the PiTFT line from Adafruit
up to the 2.8 inch model. The higher resolution 3.5 inch PiTFT requires a specially modified Adafruit kernel, which, unfortunately is based on an older kernel that doesn't have the latest hardware support and bug/stability/performance fixes (but since the Pi-Zero is based on the original Pi, that kernel should be okay).
There are other HAT type TFT screens as well, but they tend to be less well supported than the Adafruit PiTFT and require more effort to get running. They are usually less expensive though.
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?