A very simple beginners gun would be most double action revolvers. They're simple and safe, especially when compared to semi-autos. Most people who get accidentally shot are from someone who thinks an auto is empty, when it actually has a round ''up the pipe.'' (A chambered round, which stays even with the magazine removed)
A DA revolver fires by just pulling the trigger, with a hard pull for the most part, (For short range self defense mode) or you cock the hammer first then have a light trigger pull. (For better accuracy) No magazine to load up, no pulling a slide back to chamber a round first, no worrying about releasing the safety(s) etc.
A good conceal weapon is a Charter Arms Bulldog. The five shot .44 is a hand cannon. They're a short barrel that you'd expect Mickey Spillane P.I. to pack. The .38 or .357 might be better for your girlfriend to handle, as the light .44 kicks like a mule.