No offence intended, but this site urgently needs someone who knows how to run a webserver to get involved.
I've never seen a site fail so badly on so many points - WebPageTest Test - Running web page performance and optimization tests...
There are LOADS of suggestions there that could easily be implemented and would massively speed the site up.
In addition you could switch from Apache to something fast like Nginx, and the version of php is hopelessly out of date.
The very first and easiest free thing to do would be to use Cloudflare; that would take at least 50% of the load of the server and do a lot of optimisation.
Then you could add in Varnish cache - end result: 200ms page response times rather than 20seconds, net cost: half a day of the time of someone that knows what they're doing. No need to spend money on new servers.
But in short, this site isn't suffering because of visitor count, it's suffering because it's hopelessly unoptimised and urgently needs some TLC.