Picking a nearby battlegroup/datacenter is a good point, but another thing to consider is realm time.

When my wife and I first rolled toons, it recommended Drenden for us--a server in a battlegroup that was relatively nearby, but an east-coast timezone server.

We're in AZ and don't use DST, so we fluctuate between Pacific and Mountain times. Eastern is no good for us, but we didn't realize that it'd be an issue until we were already level 70 and trying to start raiding. We still stuck it out for nearly two years, but between time issues and server progression we were just unable to find a group that we could call home, and unable to recruit for our own guild at the times we needed to raid.

Being the complete and utter nerd that I am, I made a spreadsheet. We listed all of the Pacific PvE servers, recorded each realm's progression (I think from wowprogress.com, could be wrong) and checked the realm list at 6pm & 9pm to see how full the servers were. This gave us short list of about 5 well-progressed, medium-to-high population servers. Of those five, we looked a bit deeper--Alliance-to-Horde ratio, battlegroup location, the attitude on the realm forums, wowwiki article, etc. We also looked at name availability, but ultimately made a decision despite the necessity of a name change.

One server really stood out for us, so we rolled new toons and tried to get a feel for the place. Loved it, and eventually moved or rerolled all of our other toons to this server.

It was a fairly scientific way of choosing a new server, and probably sounds a bit lame, but when you're talking $25 a pop ($50 for a couple) to transfer to a new server, you wanna make sure you're making the right decision!