Never liked integrated video much. Even if there was an open vid slot for future upgrades, the bios could still cause some instability. There is also some more potential for the whole MB to fry using integrated video.
Really, the important factors to consider for a work computer are stability, upgrade capacity, cost, and useable lifespan.
If you get a integrated motherboard without an available PCIe slot, you will be looking at a more expensive upgrade should your video go out (something I have personally seen on a few systems using integrated cards). Also, depending on the nature of what you are doing, consider if there may be applications down the pike that are graphical in nature that you could be using. Much easier and cost effective to just throw in new vid cards as needed as a good cheap Duo 2140 could last as a work computer for literally a decade+. Most of our office systems were built in 1997 around a Pentium 3 128 meg RAM server. Applications we use though are mostly web based and rely more on a high speed DSL connection.
Regardless though, get a solid MB with an open PCIe slot and one of the numerous dirt cheap vid cards available and your pretty much in the same price range as a integrated solution except with more potential stability and room to upgrade.
Also, build you own- don't buy cheap E-Machines. You'll pay a bit more initially because of the OEM OSs, but you want to put in a good quality PSU like a Antec Earthwatts $29 sweet deal. One thing I do most with work computers is replace cheap PSUs that fail. Stability is far more important then saving a few dollars initially. The few extra spent building will be saved in man hours alone trying to troubleshoot hardware problems later.