Hello Abstr,
You're not very far off except that a VPS is a virtual machine which is where they take a server and with software divide it up into a specified number of virtual machines. It gives you the feel of your own dedicated server but does not have quite the resources of one and most certainly does not have the cost of a dedicated box.
If all the experience you have is with shared hosting then yes there will be a learning curve. The important thing will be to get your site/s up and running and support and people here on the forum can and will help out with just about anything you run into and of course Google is a great help too
Take a look in the tutorials section for your control panel on the forum here and you may very well find just what you need.
As far as security goes using strong passwords is of course a must and a great place to start. If you want to install a firewall (such as APF) you can submit a ticket to support and they can do it or there are tutorials for here on the forum too (I know there's one for cPanel at least) and many more available on the web. Just take it slow and familiarize yourself with SSH and the tools/commands you need to use to get what you want done and you'll be fine.