Should I use a centrifugal or axial fan for server room ventilation?
Is this a datacenter (raised flooring, proper precision air conditioning, fire suppression, etc.), or a server room (tiny space with heat producing machines that happens to have its own AC unit or duct leg)?

If you're talking about a small server room all you want is a fan that moves the volume of air you need to move through the length of duct work you need to go through, and preferably does it quietly enough not to annoy anyone.

As a general rule direct exhaust (or short straight duct runs) can use either type of fan, but for longer ducts, curved/bent ducts, or anything else that's going to increase resistance to airflow you want the extra force centrifugal fans generate.

Also as some folks mentioned in the comments, make sure you're pulling out hot air and not messing up your airflow -- cool air should be blowing in to the front of the servers, and the exhaust system should be pulling hot air from behind them.
A draft detector (or a cigarette if you're so inclined) can be useful in making sure air is going where you want it to (test with your AC on and off).  



If you're talking about a real datacenter with raised floors and precision air conditioning you I beg you not to do this (or at least don't DIY) -- Proper datacenters are usually sealed environments, and adding exhaust systems to blow off hot air has lots of fire suppression and climate control implications.  

Codes vary, but most datacenters use clean agent flooding for fire suppression, so exhaust systems have to have integration with the fire alarms (usually electro-mechanical or magnetic drop-dampers). That integration is a job for a licensed and insured HVAC contractor, because if something goes wrong your insurance company is going to want to sue somebody and you don't want it to be you :)