The purpose of the VMware VMA

There are three components you need to consider;

1. ESX Licences - ESXi (not ESX) is free but limited when free, you can't give VMs the full 8 vCPUs, don't have HA, FT or DRS functionality etc. but it works just fine with or without shared storage. If you want these functions it's going to cost.
2. vCenter - this management software costs but is the only way to make two or more ESX/i hosts work together to provide HA, FT, have DRS functionality etc. Note that the ability to live migrate guest VMs from host to host requires shared storage.
3. Shared storage - without this you can't live migrate from host to host or support HA.

So really it comes down to your downtime requirements, if you NEED HA, DRS, vMotion, FT to increase your service uptime then you need ESX licences, a vCenter licence and shared storage. If you don't need these functions you don't need any of these extra-cost items.

Oh and there are free backup solutions for unlicenced hosts, such as GhettoVCB.

vCenter Server is basically a management tool that will allow you to manage VM's across multiple VMware hosts at once. You'll connect to vCenter Server with a vSphere client and instead of one host you'll see multiple hosts at once.

You can migrate VM's from one host to another via vMotion (although with Essentials you can't do it while the VM is running, and it requires shared storage). vCenter is especially useful for the more expensive VMware licenses, to manage things like DRS, HA, clustering and vMotion. With Essentials the use is more limited, but I also have Essentials and I've still found it to be quite useful to see my entire VM collection at once.

vCenter Server runs well in a virtual Windows box. It needs SQL Server Express or better and a 64-bit Windows OS.