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My 9mm is a hi power but that is outside of your price range and the list you made. But even though it is not on your list I will suggest looking at Remington's R1 in 9mm.
I would look at a cz. I got my shadow sp-01 for about 849$ new 2 years ago, incredibly accurate and if you have medium sized hands it would likely feel better in hand than either a sig or beretta.
Get onto You Tube and looks up "travis haley hand gun grip" and watch it and do some practicing with your new gun with your grip before you hit the range.
In particular you want the gun to rest as low as you can in your grip. A key factor in this "high support" is the weak hand's odd bend at the wrist which he shows. Study that in particular.
And try not to grin so hard that your chin cracks and falls on the ground....