StaffPad and StaffPad Reader have been tested on numerous types of Wi-Fi connection configuration; from Personal Hotspot connections created by phones to industrial scale mesh networks.
For the best and most reliable results, especially if you're planning on using the Reader system in a performance-critical environment (like a live show), we recommend setting up a dedicated Wi-Fi network. This connection does not require the internet, so you could simply plug in a Wi-Fi router, set the network to be open (no password) and then instruct each musician to connect to the open network. Since it's not connected to the internet, there's not much harm in doing this, and it simplifies the Wi-Fi setup considerably.
For example, you could purchase a few mesh Wi-Fi "pucks" such as Google Wi-Fi, plug them in and simply connect to them. Without any setup, they are open to any connection, and operate at fast speeds over large distances.
Of course, if you really want speed, then you could set up a more advanced network like those find in low-latency gaming situations. Even high end prosumer Wi-Fi routers are able to create quick 5ghz Wi-Fi meshes that are easy to setup and high performing.
In a pinch, you can always use your phone as a hotspot. This works perfectly fine and has no effect on the playback accuracy. You might find that some changes and the initial connection are slower when using this method, and the total number of devices you can connect might be limited by whichever device you have running the hotspot (for example, most iPhones only allow a maximum of 10 devices to connect to its personal hotspot).
There's also some great travel Wi-Fi routers that work well, and are battery powered. For example, the RAVPower FileHub. This is a portable battery powered Wi-Fi router that is capable of creating a local 5Ghz connection whilst also operating as a power bank for your devices. This means you could quite literally use the StaffPad Reader system all night, even in the middle of a field, if you really wanted to!