Reply To: BuddyPress on hosted shared server
Shared hosting is not suitable for large community sites. Also, WP Rocket isn’t going to help much here and that is because it only supports full page caching which isn’t suitable for community sites (you can’t serve cached pages to logged in users).
If you have some experience you can grab a cheap $10 digital ocean VPS
https://www.digitalocean.com/pricing/
Then you will need to either do server side caching (Nginx, varnish, something). Or if you want to setup something more simple setup like Redis (kind of the opposite but) and then grab the W3TC Fix Plugin and setup Object and DB caching.
https://github.com/szepeviktor/fix-w3tc
As for a CDN. This can vary if you are looking to replace storage on your server get something like Amazon S3 if you want more performance run CloudFlare you could run them both at the same time if you know how to configure it.
Finally, you want to combine all of your site’s assets and do a bunch of on-page optimization.