At one time, I had been a VERY avid shooter and gun owner for years and owned quite a few guns. However, I didn't, and never had owned a single handgun chambered for the 9mm Luger cartridge. I was a hard core 1911 guy. But there is one issue that you have to face: some of the coolest handguns ever made, are 9mms.
I eventually bought a 9mm, and then another, and another..................
The ones I would pick are the same ones that many others in this thread have already picked.
In order:
Glock 17: not a good looking gun, but IMO the best all around 9mm. I view this gun as a tool. I am not "into" it. It is my everyday carry gun and for that reason, every time I go to the range (at least once per week), I fire one magazine from one of my Glock 17s at a fairly rapid pace concentrating on concentrating on the front sight, rapid sight picture, and smooth consistent trigger control. I don't particularly enjoy doing this. I do it first to get it over with and then move onto guns I really enjoy owning and shooting. If I could only own one handgun, this would probably be it. If I could only own one 9mm handgun, this would definitely be it.
Browning Hi-Power: elegant. Enough said.
Beretta 92: I enjoy shooting this gun, but I bought it primarily just because I thought that a decent American gun collection should contain an example of the currently issued US Military sidearm. It is one of a few double action pistols I own which gives me something else to play with at the range.
CZ 75: I don't own a CZ 75 and probably never will. But it looks to me to be a very nice looking gun and from all accounts I have read; is one of the best.
I guess for number five I might pick a Sig. I don't own a Sig. I once owned a .45 ACP Sig and it was a fine handgun. Again, I will probably never buy another Sig, but it isn't because they arn't great handguns. Its just because I already have more guns than I can shoot as much as I would like and I don't need another one.
I suppose one of the historical guns would be appropriate. I own a couple Lugers, a couple P38s but they don't really do much for me. The fit into the catagory of some something I always wanted, then after I got them and played with them, the novelty quickly wore off. Compared to other 9mms, the single stack magazines are a serious limitation. I have a Walther P1 that is a good shooter and is cool to look at but I doubt I would go out looking for another one. My Lugers are not real nice examples: they are servicable but compared to the other 9mms I already listed, it is near the rear of the pack.