Looking to upgrade host - somewhat unique situation

I’m running a kind of banner exchange program where i’m getting thousands of requests to a php script along with sql queries from a variety of sources (and growing rapidly) To give you an idea, the address is publicitywheel dot com.

The problem is, i’m starting to see some real slowdowns (10+ second load times) through Dreamhost, and I just don’t think it’s up to it anymore.

Can anyone kindly recommend what sort of host would be ideal for my needs? Should I avoid shared hosting (given the nature of my site) and move straight to dedicated? If not, will VPS be good enough? I’ve had my eye on Managemybox but don’t know if it’ll be overkill for what I need.

Any thoughts would be greatly appreciated.

Thanks in advance.