A "wireless modem" is, hopefully, a one unit modem / router / WiFi access point.
A modem, by itself, allows you to connect only 1 computer, and provides no
security. Hopefully, you wouldn't be getting one of those. You absolutely need
a router, especially if you have more than 1 computer.
The advantage of getting separate units is versatility. There are dozens of
models of different routers and modems, because there are dozens of different
ideas of what features are needed. As long as a combined unit offers you the
features that you want, it's good enough. As long as it's a combined unit, and
not just a modem, that is.
Chuck, MS-MVP [Windows - Networking]
Paranoia is not a problem, when it's a normal response from experience.
My email is AT DOT
actual address pchuck mvps org.