Well, first, congrats on your permit! I have not handled the Sig P320, but I do have extensive experience with Sig, and they are top quality. The FNS 9 is a fine pistol. I owned it for a while when I was working through my process to find the best EDC pistol for me. I have little experience with the HK VP9, but just ordered one. While handling it in my local gun store I can tell you it is well balanced, feels solid, and the trigger is very crisp, which is very good. I carry the Glock 19 Gen4 EDC, and I have also the Glock 17 Gen4, Glock 42 and a CZ-75B, which are all great guns. Of the three you listed, I would say HK and Sig are a step above the FNS, although FN does have an almost cult like following. I can tell you this. I am very pleased with Glock Gen4 pistols, but I am really looking forward to shooting the VP9. My cousin is a local cop and says that one of his LTs on the SWAT team has the HK VP9 and LOVES it. HK is one of the premier handguns made, but you'd really be hard pressed to go wrong with any of the three you listed.
Here's my advice. Shoot all three side by side. This will give you a really good feel for which is best for you. You should be able to find a range that rents guns, although you may have a hard time finding one that has the HK VP9 and Sig P320 for rent as they are really new guns on the market. I think the HK just became available last month. I would push the HK, but you may love a different one. Why I would push the HK is that the ergonomics are superior to the other pistols. They are the last one to enter the "striker fire" pistol, but don't let that fool you. They were actually the first to make a striker fire gun many years ago, so they know something about it. They took about four years to develop this pistol, and the trigger is what really sets it apart. The bore axis is really low allowing for easier sight picture acquisition, and the pistol is just really well made. Sigs are great guns, but they have a much higher bore axis making it a little more of a challenge to get the quick sight pic, but that is something that can easily be overcome. For one, you may like that better than the lower BA, but also the more you train with the weapon you select, the more proficient you will become with it. That's why I recommend shooting all three, or even as many as you can, to determined which you prefer more. Doing so will take a little more time, but it helps you find the best pistol for you before you spend the money on one you don't like as much as another.
Plus it is just a lot of fun! Good luck with your search!