RE: Cheap Ammo
The Handi-Rifle is a good little rifle for the money, and the .223 will be the least expensive ammo to shoot and do an excellent job under the conditions you stated. My suggestion would be that you strongly consider not skimping on the glass you put on it. Good scopes start at about $150 and go up from there, and yes, you do get what you pay for 99% of the time. I'm not saying that you must put a $700 scope on a $200 rifle, but I'd recommend that you plan to spend as much on the scope as the rifle. I'd suggest you look at the mid-range Bushnell (Elite 3200 series) or Nikon (Buckmaster or ProStaff).
Mike