For an application with the traffic and size of twitter, you're going to need at least three dedicated DBAs managing your MySQL installation (never have an even number of DBAs - it leads to tyranny), which is probably going to be spread out across a cluster of replicated servers.

You're going to have a very beefy load balancer, behind which sits a bunch of nginx installs and you'll have likely thrown CI out the window because, even though it's fast for a PHP framework, it's not fast enough for what you need. You'll be using PHP, likely with a few homebrew extensions written in C.

Or you could just use Node. It has non-blocking IO. :D

Realistically, write it on a crappy linode with the default MySQL install and your PHP framework of choice. If you ever get as big as twitter, you can worry about scaling up to that size then.