What kind of server do I need?

Well, it looks like my website has outgrown its current webhost and I'm looking to move to a new one. It's currently hosted with ProHosting and everything worked alright until about two weeks ago.

The site uses a lot of CGI scripting and mySQL databases and is now at the point where it sometimes doesn't have enough resources to run scipts, the database sometimes refuses connections due to too many simultaneous requests, and the site slowed down in general. My traffic has been pretty much doubling every month and it looks like its going to hit 10Gb for this month. I think that ProHosting has great tech support and they have been very helpful, even moved me to a less loaded server for the time being. However their support isn't 24/7, which caused me quite a bit of downtime in the past weeks and has prompted me to look for a new host.

So could anyone advise me as to what type of hosting solution I need for such site? Would I need a dedicated/colocated server? If I do need a dedicated server, what server parameters should I look for (CPU/RAM)?