Hello and welcome to the communities.
There is no way to really enter a license or anything
You go to the server's Configuration tab in the vSphere Client, and use the Licensed Features link in the Software panel to add the license. You can get the free license in the same place you downloaded the software. The base ESXi product is the same, it is the license keys that unlock or activate the features once demo mode expires.
I would stick with v5.1, especially if you are just starting out.