The G19 is a stellar all around handgun. From civilian CCW, to uniformed and plain clothed or U.C. LEO work, to home defense, the G19 is immensely popular for good reason.
For years I carried one while working in the middle east. Both concealed and in a drop LEG holster. It was an ideal all around gun for the job.
Now with that being said, throwing competition into the mix, I would opt for the 17 of the two you mentioned. Going outside of those parameters, I would go with 2. A G34 for a game gun and the G 19 for concealed carry. Either would be fine for home defense, but since your game gun is likely to be tricked out, I would just use my carry piece ( the G19) for that role as well, adding a white light to it to allow you to use your non dominant hand to open doors, grab kids, phone 911, whatever.