I agree with previous replies. Do not buy a Phoenix Arms HP22. I just got rid of one.
You mentioned that you wanted to use shot shell .22's. There is not a semi-auto out there that will funtion with the low recoil of shot shells. You will definitly need a revolver. Also, shot shell .22's are only effective for about 10 feet. After that the pattern is so spread out, you would be lucky if one pellet hit what you are aiming at.
I would suggest a revolver so you can shoot any and all .22 ammo on the market, including , shot shells.
You want something cheap? Look for a good used Taurus, Ruger or Smith. Remember, If you buy cheap,ie. unknown or low quality, they won't last and they won't be dependable.
I've been shooting for more than 40 years and have wasted enough money on "budget guns" to tell you to buy brand name weapons.
Hope this helps you out....