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How to find web hosting that meets my requirements?

If anyone wants to get some real life karma by giving a tiny non-profit pointers, please advise!

I posted a thread about our website with highly variable traffic (www.WorldOceansDay.org). The event is on June 8th, and the traffic goes from 100-400/day in the off-season, to about 200,000 trying to access the site at any one time on June 8th. It's a Wordpress site hosted on GoDaddy shared hosting and predictably crashed horribly.

From the internet's feedback, we've decided to move to a cloud server to handle the traffic, but I'm a huge newbie and I don't have very reliable mentorship, so I'm turning to crowdsourcing.

We're trying to decide between Amazon Web Services and RackSpace Cloud servers. Our sys admin consultant also suggested GoDaddy's new 4GH but I have had such incredibly bad experiences with GoDaddy thus far that I am hesitant.

From what I've read on the internet, RackSpace might be cheaper? Would AWS totally break the bank? We don't have a ton of money to spend on hosting. We'll also be using CloudFlare to cache and serve the pages since they're dynamic. I've found a few AWS & RackSpace calculators but I am not 100% on how to find those numbers... GoDaddy? Google Analytics?

AWS calc is here: http://calculator.s3.amazonaws.com/calc5.html Rackspace is on the right: http://www.rackspace.com/cloud/cloud_hosting_products/servers/pricing/?0a313380

If anyone can help, or through some miracle feels like walking me through this, I would be incredibly appreciative.