I’ve used a Zero running Jessie Lite to make a media server - for the purpose of streaming movies to my kids’ Android tablets on long car journeys. It’s powered by a USB battery pack.
I’ve used a Pimoroni USB hub (the white one with 3 USB ports and an ethernet jack at the end) hosting a USB memory stick and an Edimax 7811 wifi adapter. I used this reference to help: http://www.daveconroy.com/turn-your-raspberry-pi-into-a-wifi-hotspot-with-edimax-nano-usb-ew-7811un-rtl8188cus-chipset/.
The Pi runs
hostapd to create a wireless network
isc-dhcp-server to offer a DHCP service
minidlna to offer a media streaming service
It works fine - and can even stream two MP4 movies simultaneously. I’ve added a reset button onto the RUN points on the board. I’d like to add a soft shutdown button but haven’t spent enough time understanding GPIOs to make that work yet.