Here are my priorities in a combat handgun: 1) reliability, 2) accuracy (in your hands), and 3)power. I'm willing to give up some of number 2 and a little more of number 3 to get number 1.
There is a theory that the 9mm is inherently more reliable than the other two calibers you mention because of its tapered case (the .40 is "rebated" and the .45 is straight-walled) and its bullet profile. It makes sense to me, but I don't have any "relevant data" to support this theory... it just makes sense to me. I've had a lot of handguns, and it seems the 9mms have tended to be more reliable than some of the .40s and .45s, and more accurate than most of the .40s. I've had reliable and accurate .40s, I carry one these days as my working gun, but it seems like the ones less prone to issues were the nines. With a 9mm, you get cheaper ammo on average, and higher capacity in similar weapon platforms. I also believe that the 9mm is probably more ammo dependent when you talk about its effectiveness, but there are several choices in good, modern hollowpoint designs out there, and chances are you can find one that works well in the gun you choose. Just one man's opinion. Smarter people than I will give you a different one.