Glad to hear this wonderful news! I am happy that your hard work finally starting to pay-off.
It depends on the website or on the script you are using! If you are using some very heavy script/coding that on each site load generates hundreds of SQL queries and the web-page size is high then you will need a server with more Cores, RAM and Bandwidth.
Make a deal with your hoisting company/provider and tell them that you will need to experiment with each server plan to see which one is more suitable to your eCommerce.
plan then move to Professional
if you still have problems then switch to Enterprise
Here are some links to cheap and high performance VPS and Dedicated servers!
Virtual Private Server (VPS):