Originally Posted by SevY

Hosting is not just response time. Your high response timing can be due to several things like poor design code, busy switch port or a low tier carrier.
Besides that you'll never get a top level response unless you opt for non-shared resources such as a dedicated server or a VDS and for a dedicated bandwidth or, at least, a dedicated switch port.
If you are on a budget your best option is at least a VPS since they are hosted on non oversaturated boxes like the ones for web-space hosting.
If you are in Europe, my advice is to opt for Kimsufi's cheap VPS (an OVH reseller). If you're in US my advice is still OHV but with they'r "USA Eco VPS" solutions.
If you don't like OVH you can opt for Leaseweb VPS or similar.
Avoid things like godaddy hosting 1&1 hosting and other domain/cheap providers giving out "unlimited bandwidth" and "unlimited space" for $0.05/month. It's all BS.
The key is: your resources must be controlled by you.