It depends on three main factors:
1. Website traffic
2. Code optimization
3. Server optimization (using Nginx, varnish caching, etc)
It is entirely possible to only have 1 visitor on your website and your VPS becomes overloaded due to poor configuration of the script, having 1,000 products on your main page, etc.
I would ensure that wherever you go that you have a managed VPS or dedicated server so that they can analyze your usage and make system level tweaks to improve the performance of the website.