Eagar would be the cheapest option for property. Then show low then payson. Payson is out of control on land prices. Most snow is gonna be show low. Sunrise ski resort is abiut same distance from show low as from eagar. Payson would be about a 2 hour drive to ski. Any of the three you can be chasing elk within 20-30 min. Payson would offer more opportunity at upland game opportunities (gambels quail in the desert). Any of the three are close to fishing but Payson would be closer to the big lakes like roosevelt, canyon, apache, saguaro.
Could also look at living in Heber which is between show low and Payson. Also pretty expensive land there and much smaller than any of the three places you mentioned. Snowflake may be an option. Land is cheaper, less snow but you're a little ways away from the lakes, skiing and a lot of the better elk country. So lots of things to consider depending on what's more important to you.