You are going to get recommendations for just about every target style .22 out there,,,
But unless you want to spend more than your stated amount,,,
There really are only four to look at.
If you have largish hands and want something stylish,,,
My opinion is that you should look at the Browning Buckmarks,,,
That particular pistol comes in a boatload of different configurations.
I love my Berettas but because of your large hands,,,
The slender grips on the Beretta NEOS might not be a good thing,,,
Even though they do have a very unique Buck Rogers Space-gun look to them.
I've only fired the S&W Victory a few times,,,
Very nice performer but for some reason my mind said "meh" to it.
I do own one Ruger Mark-III and a pair of 22/45's,,,
All of them have more precision than I can utilize effectively,,,
The 22/45 mimics the grip of a Colt 1911 and would probably fit your hand better.
As to the Mark Series and the 22/45 series,,,
I would highly suggest the newest Mk-IV versions,,,
The take down is much easier than all of the earlier versions.
Anyways, there are more expensive pistols out there and some will have more inherent accuracy,,,
But I guarantee you that any of these four will be great pistols for serious range shooting.
Happy hunting for your first pistol.
Aarond
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