Note: those are some pretty generic suggestion as the question is pretty open ended as it is. If some more specific need arise, please try posting another question so we may try to give you more focused help.
Since you said you are new to SharePoint development I would try to avoid SharePoint specific solutions like using External Lists and instead try for a more basic solution.
I don't really know what your skill level with other technologies is, but either case I would probably start from a Visual Web Part farm solution created in Visual Studio, since it should be the most basic option if you never worked with SharePoint before (if you are a total beginner I would advise against attempting the creation of a SharePoint app/add-in). From there you should be able to either create a basic asp.net form using the SqlDataSource component and the AspGrid or do something a little more complex with a framework like Angularjs, maybe using Entity Framework to access the data.
That is, assuming that you really need the info to be stored in a database. Since you seem to be pretty new to development and probably would prefer an "out of box" solution, avoiding any custom development work when possible, I would suggest you to consider putting the info in a SharePoint list instead. Your requirements seem more along the line of providing internal support than creating an actual tool you would want to sell to some client, so probably you could sacrifice the "look" of the tool for something more simple and less costly from a time/work development cost viewpoint.
Just create a custom list from the SharePoint user interface and add some column manually: a text "Key" column, a number "max available licenses" column and a "used licenses" number one. Then, create one more calculated column that displays the difference from the max available and the used licenses ones and you should be set for the time begin. You can use the standard edit form for the list to increase the number of consumed licenses as a basic solution, and when you have some more time and experience you will be able to create a more friendly interface.
As an idea, the buttons could probably be added to the list view for the custom list using some JSLink tricks, but you should be able to live without that for a while. And if the need arises, you could also try to post a more specific question here.
