What server configuration and database should I use?
This site, is a question and answer site, not a mentoring site.  

You are already taking a Database Design class, which is much closer to the mentoring that you are seeking.  Also, you must have instruction materials that will explain at least the basics.

Questions are welcome, but you will get better results by:


Working on the problem yourself first. 
Describe briefly your overall project.
Focus on one or two points, not a sweeping discussion of your project.
Clearly describing the problem that you are currently trying to resolve and what you have already tried.


General questions about databases, costs, et cetera are things that you need to study up on in advance. You must know the basics or your questions will get little useful response.

Search DBA Stackexchange and other sites to see what answers are already available to you.  You often just need to search.

Specific responses:


SQL Server Express 2014 can be a fine, fully featured database server.  It does not have all the auxiliary tools that the more expensive editions.  There are limitations: only uses one CPU, no single database can be bigger than 10 GB, the use of memory is limited, and so forth.
It is better to keep the domain controller and the SQL Server on separate machines, even if virtual, because of the increased exposure to security problems. 


Your goal to create a simple system for a small group of users is a fine place to start.  You will learn a lot in the process that will help prepare you for bigger tasks.