Wired is faster. Even if you buy a wireless router, you can still use wired, becuase they usually have 4 wired ports.
If the computers are close, I would recommend wired and gigabit if you can afford it. Get a router with built-in firewall for maximum safety.
Tom's hardware has some router charts you can consult prior to buying.
Wired is almost always quite a bit faster. The "108 Mb/s", "125 Mb/s", and even "54 Mb/s' are signalling rates well above what you would see in real data throughput, even with short distances and an interference-free environment. This is known as "marketing crap".
Wired can come very close to its advertised rates.