Windows Server 2012 R2 AD Domain

I have a client that is in need of purchasing a server to maintain a financial package database (Peachtree) and user files (word, excel, pdf, etc.)  They estimate 5 to 10 people will eventually need to access this server, but initially it will only be 4 people.

The server will be Dell T320 server with a single XEON processor, 16Gbs of RAM, and (3) 600Gb RAID drives for the OS and data.

They have no need for Exchange on-premise or Office365 since they are very happy with their Google mail solution.  

I usually prefer setting an AD domain for offices that have a server and at least 5 users, but at the same time I am thinking this office could simply use this server as a member server with network shares, etc.  

I am still inclined on setting up an AD domain, but I am not sure of the actual AD domain name to use.  I have always used a .local domain, and now Microsoft recommends using a valid .com name instead.  Microsoft keeps going back and forth on this matter.  

So the domain name for this company's website and email is long, let’s say something like (www.automatedproductsgroup.com).  They own this public domain, so am I supposed to setup the AD Domain Name as automatedproductsgroup.com?  I want to abide by Microsoft's naming requirements, but this name seems a bit long and not right.  I simply wanted to use "apg.com", so it abbreviates the name, but they do not own this public domain name.  I was simply thinking of using apg.local instead to avoid all of this, but I am not sure what kind of problems a .local domain name will cause down the line.  

This office also has a need where the owners (3 people) will need to work remotely and access the financial application and user files.  They will have laptops that travel with them and are used in the office.  So they will not have desktop computers to remote into while out of the office.  They have another facility setup across the country that was setup be a local consultant as follows:

They use logmein himachi to setup a VPN.
Once the VPN is established they can access network shares for that remote network.
They have a Peachtree icon on their desktops that opens slowly, but eventually allows them to open the company file from the peachtree server share residing on the remote server.  

The problem is they do not have desktops in the office to RDP into, and have a dire need accessing their Peachtree database.  Right now I am not concerned about the server setup at the other facility across the nation, and I am concerned about providing a more robust RDP solution at this new facility.

Since three people may need to simultaneously RDP and access the same database, I was thinking of purchasing a 5 pack license of Windows 2012 RDP CALS (approx $400.00).  I would think they do not need a VPN connection, and be able to RDP to the public IP of their router, and have their router forward all RDP requests to the server.  I believe Microsoft RDP is a secure enough connection without the need of a VPN.  If so, all they would need to do is enter the pubic IP in the RDP connect host.  I also need to find out with Peachtree whether using their application on a terminal server is an issue or even supported.

So, let me breakdown what I need help with:

1.  Setup a simple member server instead of an AD domain?  Thinking an AD domain the best way to go.

2.  The internal AD domain name.  This companies public domain automatedproductiongroup.com.  Do I need to use this actual name since they own the public domain name or can I abbreviate it to agp.com.  The do not own the public name apg.com.  Or simply go the .local approach apg.local to make things simple.

3.  A minimum of 3 people need to RDP this new server.  They currently use logmein himachi as a VPN solution to access network server shares and access a Peachtree database.  This solution works fine for file shares, but accessing the Peachtree database is a bit cumbersome and rather slow in my opinion.  Possible resolution, purchase and setup Windows Server 2012 RDP CALs, and instruct the users to enter the public ip of the router to directly RDP to their server (terminal server) without a VPN.  

4.  Based on the server hardware config mentioned above, is it configured with enough resources (processor, RAM, hard disk space) for a server that will be the sole AD domain controller, DNS, DHCP, terminal server, TrendMicro worry free business standard server, printer shares, file shares, and Peachtree database server for 5 to 15 users.  Terminal services will not be used by all employees.  Not sure RRAS maybe included in the mix should VPN access be necessary.

Please forward your suggestions and recommendations.  I just want to make sure I set things up looking at the future and not simply to quickly get things going.