From Windows point of view, the difference is whether you intend to share anything at the windows network level with other computers. Typically, you could share disks and printers, discover computer and resources or allow your own computer and its resources to be discovered.
If you only use the laptop and a phone as router, it is unlikely that you could use a shared printer or shared disk on a local network, or share your own resources, so you should declare the network as public (or untrusted with your terminology)
The only use case for declaring it as trusted (home or work) would be if there were different laptops (your own, your wife's one, and your child's one) all connected to your phone. In that case, if you wanted to be able to easily share disk resources, you could choose home network. But this could be a security risk if the wifi access is not protected with a secure protocol (WPA2 and not WEP) and a non trivial password (not the default 12345678)
TL/DR: except in very special use cases, you should always declare you phone network as public (untrusted)