Yep, I think the jury is back and the verdict is the 120gr. TC.
For the OP, I wouldn't get hung up on the "short barrel" criteria. The 9mm is a high pressure cartridge and the barrel length isn't super critical.
The 120gr TC design seems to be the most "universal" bullet for 9mm. That profile will feed & function in most 9mm platforms. The weight is exactly where it needs to be and it is capable of decent accuracy.
It's all been said before but since we're here.......
The groove diameters of 9mm pistols are all over the map. So it's often beneficial to size your bullet for your gun. While that advice is always true, it is particularly applicable when we are talking about 9mm pistols. And, 9mm pistol barrels often run a bit on the large size. In theory, the groove diameter should be .355", in reality they are often closer to .356"-.357".
The 9mm Luger cartridge does its best work with bullets between 115-125 grains. Nuff said there.
I tend to run my 9mm cartridge overall length on the long side. The limiting factors are: Will it fit in the magazine?, Will it chamber?, And will it feed and function?
For just punching holes in paper and ringing steel, I have never found a powder that will work better than WSF.
If you're seeking the maximum velocity, there are some other choices but that's a whole different ballgame.
Good Luck