Seeing that you Want something within a cost limit bullet wise,
i'd highly recommend the .223, .222 is just below this but bullet choice is limited and not readily near as available as the .223, unless your gonna take up reloading, then i'd recommend the 22-250, if not i'd go .223,
WHY....
look at the sheer choice of rifles available to you....
choice of ammo is vast...
price of ammo is good if you shop around....
try a few different factory brands and weights and see what your gun likes then buy bulk and get it cheaper.....!!!
.223 will cover your range limi