The Internet is a Wide Area Network. Unless you have an Internet connection going through a router into a Local Area Network, then you will have to connect to the Internet via a modem (either dial up or broadband). The Computer you are considering may have an analogue (dial-up - 56K?) modem fitted, but if not then you can get them to fit in the case if it is a desktop or tower type, or a plug in (PCMCIA) type for a laptop. For most types of computer you can get Universal Serial Bus (USB) types that stay outside the computer and connect to sockets on the machine.
A Network Interface Card (NIC) is only necessary if you are going to connect to a local network, like wires or radio around the house or office.
If you do not have a local network running around your house or office, then the NIC Ethernet 10/100 connection is redundant.