I think modem is a thing of the past. If your modem serves you
well maybe you can sttill use it. If it outgrows your needs and
application maybe its time you get one that suits you and have
wireless capabilities. Foe me i still prefers wired connection
mainly because i don't trust my data in the air and my room is
small and large enough for my wires.
The main differences between a router is some form of hardware
firewall installed and offers some form of protection for your
identity when online. Modems are build in the router which offers
more functions like broader data bandwidth transmission with the
RJ45 ports.
Dlink and some common brands mentioned should do fine. If you can
use it for a better number of years it wouldn't matter if it costs
a few dollars more than the cheapest router on sale. The cheaper
router may go faster than the more costly one resulting in you
spending money again to replace the bad unit earlier than
expected.
