We just launched our mobile app (social/fitness). What should our server requirements be to maximize performance when we move out of Beta?

In case Godaddy does not offer you a bigger data transfer plan, you can move to Heroku. They let you choose how much efficient you want to configure your server

I recommend something like Bluehost or Rackspace. They offer programs that scale with your need so you don't hit a cap in the middle of the month.

I am an affiliate of Bluehost (www.shaunnestor.com/recommends/bluehost) but that does not change my endorsement of them nor does it raise the price you pay.

I fear that you may hit a cap with GoDaddy if your site experiences a rush of traffic or server demand. They'll send you an email letting you know you've reached your maximum and your site will be useless.

I'm happy to talk more, if need be. Just schedule a call here on Clarity.

-Shaun

I have built and helped build more than a couple service backends for mobile apps.

You are much better off with a PaaS offering like Amazon's AWS/EC2, Heroku or Microsoft's Azure.
These services allow you to keep your costs low while you still haven't achieved scale and make it really easy to scale up your backend when you do.

Do let me know if you have further questions and all the best with your business.

I've been running a mobile app development company for the last 6 years. We've found the most reliable option is AWS (Amazon). Its got lots of options for scalability, load balancing, server alerts etc.
It really all depends how quickly you scale, even when you get out of BETA, you may still be fine for a short while.
However, if you are planning to do a large advertising/marketing push, I would make sure you are on Amazon before doing so.