I found my longer barrel P22 was quite accurate. I could routinely hit clay pigeons with it at 50 yrds. The key I found was try different ammo till you found what it liked and then keep the barrel tight. Mine tended to loosen during shooting.
I have a Gemtech Outback on a p22. It is only ammo sensitive with subsonic ammo which gives little gain. I run Aquilla Standard velocity and any other standard velocity should work fine. The subsonic rounds will work but you loose some reliability and supersonic speeds are not normal out of a 22 pistol anyway.
As much as I love the Gemtech I am about to order another 22 can and that will be a SWR just need to make up my mind on which. The Gemtech is less money and possibly better value.
Have you purchased an NFA item before? A 22 can is the perfect way to start.