Here are a few quick network checks I do when I go on-site with customers.
First, I do a ping to measure latency – LAN should respond in less than a few milliseconds. Next, I do a PathPing (sends a burst of 100 ping packets at each hop, then measures how many come back) to determine if there is any packet loss, then finally I do a 100MB file copy. On a healthy 100Mbit network a 100MByte file should copy in about 10 to 20 seconds. On a healthy 1Gbit network a 100MByte should take 3 to 5 seconds to copy. If the copy is taking minutes, then you know there is a problem. Every once in awhile I come across a network where the auto detect feature of the network adapter auto detected to 10Mbit half-duplex which explains the minutes to copy.
I do these tests at nearly every customer site I go to and they are low overhead tests.