You get right down to it, rocks, sharpened sticks, snares, and instruments of like import are about as cheap as you are going to get. Not too practical for Yotes, but they fit your criteria of cheap.
Just do a little research (like you are doing), get what you want ('cause you will shoot it more and ultimately be more confident and happy with that choice), get what you can afford (you can always trade for or purchase another caliber later), and practice, practice, practice.
I don't know what "huge price difference" you are describing between bullets. I recommend that you consider logging on to
www.midwayusa.com, or
www.midsouthshooterssupply.com (a GBO Sponsor), or any of the on-line supply houses and check the prices of the calibers you want to consider.
I recommend that you consider reloading your own brass, primers, powders, and bullets on your own press, with your own dies. You WILL shoot more as a reloader and in the end spend less than paying the supply house retail and its inherent mark-up for the same number of rounds.
If you practice and are confident then whichever caliber you choose will be suitable for varmints as well as deer. Shot placement is the critical element and a confident shooter will ALWAYS hit his mark.
Good hunting.