The best hosting solutions for Prestashop are definitely dedicated servers, VPS, or cloud servers that you have to optimize to run your shop. DigitalOcean is one of the cheapest and fastest VPS, but you will need to have a sys admin on your side to configure it.
If you want a pre-optimized DigitalOcean server then you can go for Cloudways, they have servers with Nginx, Varnish, Apache, Memcache and Redis with MySQL or MariaDB. They also have 1-click installer of Prestashop and 24/7 live support.
Other option is for you to hire a Prestashop expert who has experience of setting up dedicated servers for it.