VPS is the acronym for Virtual Private Server. A VPS runs on a physical computer in a data center but shares its immense capacity with other virtual servers. This way every user has part of the resources that the physical server offers.
From the perspective of the user, however, the virtual server acts as an independent computer with its own memory, hard drive, network connection, IP addresses and administration. As the administrator of your own VPS, you have full control over it while not affecting the VPS of other members.
Example cases of when you can use a VPS efficiently are if you need:
All you need to do is fill out this application form and you will gain access to your own virtual server within 24 hours. Then you have one week to pay the membership fee. It is up to you to decide how you use your server, what you install on it and how you manage it.
A Linux distribution (distro) is a specific operation system built on a Linux kernel and other open-source software. Distributions differ in software management and certain utilities. The software in each distro, however, is always the same. If you have no idea what distro you should choose, pick Debian or Ubuntu. Both are very similar and both have the support of a large community online. You will also be able to find the most tutorials for them.