Sean, welcome to the forum. Congratulations on your excellent family heirloom WW-II bring back Luger.
Here's a link to our FAQ document:
http://forum.lugerforum.com/showthread.php?t=13121
It has a wealth of detailed Luger information, and it's free from our forum.
If you have a holster that goes with the Luger, look in the magazine pocket. It might be with the holster.
If you find it, don't store the Luger in a leather holster.
You have a Mauser made Luger. It was produced in Mauser's building "D", at Oberndorf an Neckar, Wurttemberg, Germany. This is South and West of Stuttgart.
Your Luger was made later in 1937, and has both the rust blued finish and the "hump" shaped Mauser Luger frame. These are very well made pistols.
The stamps are military contract inspection and acceptance markings and proof marks.
You can disassemble and re-assemble the Luger without a magazine. Just be careful and don't lose parts.
The takedown lever spring is a small flat "L" shaped spring with a section in the center milled away in a curve. Tom (LugerDoc) can provide some for you. Don't try and shoot the pistol without this part properly installed.