Actually, the problem of not being able to scan over the network is
because the OP doesn't have a real network scanner. The HP Deskjet F380
AIO is a simple consumer-level printer costing roughly $149 USD. Network
scanners cost many thousands of dollars and because of the cost are
normally leased from a business machines company monthly. These scanners
are used with a server (or pseudo-server in small networks) where the
scans are kept.

I expect that the OP's wishes for a particular router might be similarly
misguided. Most ISPs have their own requirements for a modem that works
with their system and it would be smarter to wait until the DSL service
was actually purchased. There are a lot of DSL modems which are a
combination modem/router, particularly the ones for businesses. Even the
ones for consumer-level DSL have got both wired and wireless
capabilities. I've never seen a modem/router that had a place for a
"wireless pen drive", whatever that may be, because why ever would you
want to put a pen drive (USB thumb drive?) into a router? No reason at all.

The OP should rethink his needs. A common DSL modem/router will have 4
LAN ports along with its wireless capability and a network-ready printer
can easily be connected to one of them by ethernet or, like many AIOs,
connect directly to the network wirelessly. He still won't be able to
use the scanning function of a consumer-level AIO over the network, though.

Malke