Virtual Private Server advice - MySQL Query Cache? Keep Alives?

We've transferred our website from shared hosting to a VPS and, to our surprise, the website doesn't load anywhere near as fast on the VPS! :(
http://212.48.71.232/website/indexHOME.php

We are totally new to virtual/dedicated servers and server management and, were it not for the fact that we need an SSL certificate on the domain, we wouldn't have bothered!

Thing is, this is a straightforward PHP/MySQL website and is, and will always be, the only website on the VPS so it's not like it's competing with other sites on the server for resources. Here is the server spec:

CPU Cores
1 core

RAM (Memory)
1GB

HDD (Disk Space)
50GB

We were directed to the following page for tweaks that we can do on the server:
http://bobcares.com/blog/how-to-increase-your-server-speed/

...but this requires "Shell Access", which we have no idea about.

Can I ask for your advice in terms of how we can improve things? We have cPanel and WHM access to the server, but a lot of the options are just completely alien to me and I don't want to start tinkering. We were told about a couple of things though, that sounded relevant...

1) MySQL Query Cache - is this something that's written in to the SELECT statements?

2) Keep Alives - no idea, but we were informed by the VPS provider that these were "simple" (they can help no further than that though as it is a unmanaged server)

Another option is, of course, spending more money on the hardware but would that make a significant difference or is the issue more related to web page / database / browser functionality?

I'd appreciate any advice you could offer.
Thank you.
NJ