yes I am using a shrared hosting before with this script but I always reach the cpu limit and I need more resources.
Well... In that case, i'd suggest just upgrading your shared hosting plan... From what i've read in this thread, your app will run 1 query every 2 seconds... It depends on the query, altough, in general, a normal shared host should be able to handle 30 query's/minute... Once again: it depends on the query itself... If your shared host cannot handle 1 query every 2 seconds they're either very cheap and very low-end, or you should have a good look at the query you're running.
It's just that when you say things like "currently I didnt know how to manage VPS and dont know how it works does vestacp panel is free to install?" I'm afraid that running your own VPS might be one step to much. Installing, securing, updating and managing a VPS is something for which you need at least a little bit of experience.
Don't take this in a bad way, i'm not trying to hurt your feelings... Having no experience with VPS's, linux, LAMP isn't something you should feel bad about, but you should be carefull starting a website on a VPS you've configured yourself if you don't have any experience.
At very least, download oracle VM virtualbox on your pc, install debian and try to install a complete LAMP server using the console.... If you cannot make it run in virtualbox, there's no sense in ordering a VPS.