1937 S/42's are pretty common, for an uncommon gun
"If" it hasn't been reblued, and "If" the serial numbers all match, then it becomes dependent on the remaining finish. Some of your pictures make the finish look a little tarnished, as though there's been some rust here or there. Hopefully your next set of pictures will clarify this. That could be the deciding factor on a final price. very rough ballpark until all these variables are known would be, in my less than expert opinion somewhere between $1000 and $1600 compared to other S/42's I've seen lately. As reference, a pistol that is reblued, or mismatched has little collectors value and is refered to as a "shooter" and they top out at about a grand, with some pretty nice ones selling for about $800-$900. So being as yours is all matching, it's worth at least a bit more than that (if it turns out to have the original finish). From what the pictures show, all other things being taken into account I'd say it's probably closer to the $1200-$1400 range. Early S/42's with the strawed componants (Strawing was a sort of controlled heat discoloration of the metal into a goldish color in lieu of blueing) generally bring in a bit higher price than their all blued bretheren, but the finish on yours doesn't look all that perfect (not trying to be mean, just honest) from these pictures, and so I think a frank and honest price would be somewhere around $1300 +/-
But as you can see, I'm a bit of a newbie here, and this is only a very semi educated guess.
One lasts thing I'd like to add, is that you really, really, REALLY should do what you can to keep it. It's a family heirloom, and once it's gone, and the money pays a bill here or a car payment there, it's gone. FOREVER. Your Dad held onto it for all these years, so it clearly meant something to him. And you mentioned the fun you had shooting it with him, those memories will always be a little more "real" when you hold this piece of steel and wood. Without it they will just be memories, and even the best memories fade.
I don't know your age, or if you have any children, but even if you do, and they aren't interested in it, who's to say their kids may not one day be? Or theirs? The value on these things is only going up. The Third Reich is out of business, and won't be making any more of these. It is a family link to the most significant historical event of the last 100 years or more. And you, your kids, your grandkids can hold it, even shoot it. When it's gone, that's it...You will always be able to get more money, but you won't be able to get another "Father's" Luger. Sell the others. Keep this one, it's the one which seems to be the jewel of the collection.