"Inexpensive" is pretty limiting. I have great fondness for many of the cartridges listed by others, above. However, when ammo cost is a factor, the popularity of the cartridge is a major factor.
30-06, 270, 243, 308 are all very popular. All will do the job you specify. I am a big fan of the 7-08 but factory ammo tends to be big money for premium hunting rounds.
There are a lot of reasons to choose something like a 7-08 or 30-06 but, all things considered, 243 is hard to beat.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.