I do a lot of pin shooting with a 9mm. I have also done some "private testing" and here are my suggestions:
A good inexpensive 9mm pin round is American Eagle (i.e., Federal) 147 gr FMJ rounds that are flat nosed. The factory item number is FAAE9FP. They are currently $7.91/box of 50 from Natchez (www.natchezss.com
You want to avoid the typical jacketed round nose bullets b/c they penetrate too well and therefore, don't knock the pins off very well.
Hollowpoints don't penetrate the pins as much as jacketed round nose bullets. Also, if you hit the pin towards the side of it, the hollowpoint bullet grabs the pin and spins it. This is good because it rolls off the table easier. For inexpensive hollowpoints, you may want to try CCI Blazer 115gr ($7.99/box of 50) or Sellier & Bellot 115 gr (not listed on their website but, it is in their print catalog; I think it's about $8/box of 50) from Natchez. I think it is more effective to use a hollowpoint rather than a flat nose bullet.
All else being equal, you want high *momentum* (bullet mass X velocity), not necessarily high energy (bullet mass X velocity squared). I have chrono'd the Winchester White Box 115 FMJ and the AE/Fed 147 flat nose bullets I mentioned above and they have almost exactly the same momentum. But as far as effectiveness in getting pins off the table, the AE/Fed 147 flat nose is significantly better from my testing.
If you are curious, I used to use the AE/Fed 147 flat nose rounds, but am now using 124 gr +P+ Hydrashok's. Both are good but, they are still just 9mm's . . .
When you get really accurate, don't aim for the center of the pin. Aim a LITTLE above the fattest/widest section and a LITTLE to one side. This knocks the pin over and rolls it off the table better. Hitting it dead center (in the fattest part) does not knock the pin off as well.
Don't forget to have fun!