Congrats on the new PT111. The assembly should not be bad, since your new to the gun world it will just take some time to get used to how it works.
Get yourself some snap caps and practice with the thing at home. Work on your grip, trigger pull etc.
I have had one in stainless with a 12 rd capacity that I have carried for a couple of years. I have no problems with it, and at the price you got it you did really well.
And yes, the 9mm luger and the 9 mm parabellum are the same caliber. Both are 9x19 ammo. You can't use 9mm makarov or 9mm shorts(.380) in it. Most anything you see listed as simply 9mm should be right for you gun.