A:
I can't 100% guarantee my answer, as I'm not a professional at these types of things, but I think there are two possibilities.
1. Based on your Property Manager's statement, I'm thinking your housing complex may have free internet, but not free WiFi. This means that the internet is activated and runs with wires into your home, but there is nothing to broadcast the signal wirelessly. In this case, you probably only need a router, but that could depend on exactly how the whole system is set up. If it were me, i would pick up a router and plan for it to be sufficient, but i wouldn't be shocked if I ended up needing a modem.
2. If the complex has free WiFI, as in something somewhere is broadcasting a wireless signal you can access, I wouldn't expect you need a router or a modem as long as the device you want to use has an antennae for the WiFI signal (i'd be surprised if any modern smart phone or laptop doesn't have this capability).
Overall, my hunch is it is situation number one and that you'll only need a router. If this is true, you should have a wall-jack that you can plug an ethernet cable into and then the other end into your router. most routers come with an ethernet cable, but its usually only a few feet long.
Hope this helps