There are some things you should consider if you are going to go wireless. If your computer is a desktop computer, and is always in the same spot, and if the modem is very near the computer, then wired would be the best option. If you have a laptop computer, or plan on purchasing one, or other desktops for different rooms, wireless would make connecting those other hosts easier. NOTE that wireless WILL be more expensive that a traditional wired connection. If you only have 1 computer, and have no plans on purchasing more, I would go with wired only... if you are THINKING about getting more computers, you can get a WIRELESS router, and connect to it with a wire, and turn off the wireless function until you get more computers that would use it... It all depends on what you have, and what you think you will need.
MOST computers come with NIC cards already, wether it is an expansion card on the motherboard, or built into the motherboard. An ethernet jack on the NIC card will like like a phone plug, but wider.