Welcome to SitePoint!
I'm sure you're aware of the three general classes of hosting accounts (four if you consider "free hosting" where you're advertising the host): Shared, VPS and dedicated. Each has its own pros and cons with cost being a major determining factor.
Shared: Generally a use as much as you can (within limits imposed by the host for usage constraints), blacklisting for the SPAM sent by others on the shared e-mail system and lack of the ability to alter the Apache or PHP services (because they're affect others on the same server). Lowest cost.
WebHostingBuzz offers what I believe is an unique feature ("Specialized Hosting") in that they tailor some shared accounts to specific CMS packages (which are generally so memory intensive that they fail on shared servers). Check this out if you have problems with a CMS on another host.
VPS: Partitioned to allow changed to your Apache and PHP but the downside is that the dedicated RAM and CPU usage is limited because it's shared by the other VPS accounts on the same server. Moderate cost (adjustable UP depending on the dedicated RAM).
Dedicated: You "own" the server and are free to make any alterations you want. Obviously, the RAM and storage are fixed (but adjustable) on the server but there is no "burst" capability as there is with a VPS (when the shared accounts are relatively inactive). Expensive.
That's a simplistic run-down for you which I trust will help. From your limited information, I'd guess that you're in the nether world of a CMS overstepping your host's imposed limits (to allow other shared accounts to run, too). If that is the case, a look at WHB's Specialized Accounts may be in order. The alternative to that is a CMS with ample resources (far more than the minimum accounts out there) or a reasonably sized (remember, you're running the account management programs, control panel, Apache & PHP, etc., and storage must be monitored else your log files will quickly exceed storage), dedicated server.
I've posted my checklist for selecting a new host (a search of this board should find it - otherwise, ask for it to be repeated ... again) but, with three WebHostingBuzz accounts, I can heartily recommend them for their great hardware, excellent and knowledgeable support staff and very reasonable prices.
I would also echo Tobias' comments above. :tup: