Your second decision factor is whether to use an internal or external LAN adapter. You're generally constrained to use an external adapter with a laptop computer unless one is already built in, but you can go either way with a desktop computer. External adapters are easier to install because you don't have to open the computer, but unless they use the PCMCIA/Card Bus/PC Card interface (see the next section), they'll be limited to at most 10Mbps. Few desktop computers have a PCMCIA/Card Bus/PC Card interface, so if you're using 100BASE-T network technology, you'll want to pick PCI internal adapters.
Because external adapters amount to extra electronic bits and pieces on your desk, they are also more vulnerable to being knocked around and broken. Internal adapters are safely enclosed by the computer case, with the cabling at the back of the case.