Not looking for an ammo advise per'say, but what should be expected. As a general rule is the .22 magnum more or less accurate than a .22 Long Rifle. Yes, just cheapish ammo, not $32.00 a box ammo.
My point of reference is that today I was shooting my S&W Model 17 that I had reamed out to .22 Magnum. It has an 8 3/8" barrel and (today) I shot both Long Rifle and Magnum cartridges through the magnum cylinder and both did very well (By my standards).
So my question is: As a general rule is the .22 magnum more or less accurate than a .22 Long Rifle. All things being as equal as possible.