Not being a bullseye shooter, my USUAL interest is groups around 3-4", at whatever range I'm shooting at, but tolerating up to about 8" groups if I am going fast.
The best way I have heard this described is "fist sized if possible, outstretched hand sized if necessary".
At 10m I don't have too much of a problem doing 3" groups and can probably fairly reliably keep it around 2". At 25 I don't find it all that easy to do 6" groups but I probably can 80-90% of the time.
But then I shoot glocks and am more concerned with "effective" than "pretty". I never measure my pistol groups and I don't shoot slowly except as part of accuracy drills, so it's pretty possible that I could do 6" at 25m 100% of the time. I rarely slow down enough to check, so I am just trying to be realistic without overestimating my capabilities here.
Anyway, as you've discovered, shooting pistols well is a lot harder than shooting rifles well. Start with your target around 5-7m and go from there. Trigger press is 80% of the game and all the standard technique stuff is really just methods of getting a good press while keeping your gun pointed in the right direction.
Balance an empty case on your front sight and press the trigger on an empty chamber. When the case doesn't move, you're doing it right.
Grip the gun right:
1) get your strong hand as high on the gun as you can. This will help with controlling recoil. Point your thumb straight up.
2) take your support hand and hold it straight out. Now rotate it 45 degrees and point your thumb straight forward. Wrap this around your strong hand. Now lay your strong hand thumb along the weak hand thumb.
This will give you maximum traction with the gun. If it feels awkward, that means you are doing it right. You'll get used to it. Keep your hands high on the gun.
Now line up your sights on the target. Don't worry about precision or whatever. Just get on target. Zen your head out like there is no gun and just tune out on that front sight. Press the trigger like the empty brass was still there on the front sight. Forget that it's going to go off...ignore the fact that you are making bang sounds, just erase your brain and mechanically press the trigger as smoothly and calmly as possible.
If you do this, I guarantee you will come back and say, "actually, shooting a pistol is pretty easy."