Hi Colton,
First, there isnt really such a thing as Proper Arabic, or slang Arabicq, its Standard Arabic and dialects
Standard Arabic is like the mother language for all Arabic dialects, we all know it, we all read and write it, but its not the communication language we use, its what you hear on the news on TV, or read in most newspapers.
As for the dialects, each country has its own dialects, but generally speaking, we could have 4 categories:
1-Shamy , spoken in ( Lebanon, Syria, Palestine, Jordan ).
2-Maghreby, spoken in ( Morocco, Algeria, Tunisia ).
3- Khaligy, spoken in all the gulf countries ( including Iraq, with small differences ).
4- Egyptian, of course spoken in Egypt only.
Egyptian is the most common and widely understood dialect of all of then, due to the media effect, and the mass number of Egyptians living every where. I'm sure your gf's parents will be able to understand- speak to a good level.
Standard Arabic will be understood as well, but it will sound strange, since its not the daily language used, but also a good choice, they will see your effort and appreciate it for sure ( since Standard is not easy to study at start ).
Learning Iraqy dialect would be ideal of course, but there are many resources for that I'm afraid.
I hope this helps !
Hala