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MineCraft Servers ... are barbariannetworks.com good?

I am not familiar about the host you are asking about. Still recommend you to do a comparison research. It will help you to make a notion of the hosting market.
Take a look at these hosts: Okayservers.com and Superbithost.com - many webmasters appreciate them for getting game hosting solutions.
Compare them and choose the best.
 
What I want to say is that when I contacted barbariannetworks.com support to get all the things cleared, they answered very fast in professional manner explaining me everything I needed to know in details. My sites have good uptime and speed upload and download of pages is perfect.