Ethernet is a protocol, IEEE 802.3. To connect to a network (LAN/MAN/WAN) using ethernet, you need a Network Interface Card, NIC. A modem is a device that, put simply, will connect to a dial in system, using PPP/SLIP/etc...
If you want to dial into something, cable or DSL, you will need a cable/dsl modem, if you want to dial over a phone line, you will need a phone line modem.
For ethernet cards (NIC's), stay away from realtec if you can, they tend to have problems, tulip based cards, D-Link, are pretty good, but the best tend to be Intel cards, I have seen that they have the best buffer speeds, and internals.