Check the guidelines for you fair, they might have restrictions on what species you are allowed to show. I can only really comment on Coturnix, as that's what I raise (got my first eggs off eBay and hatched them at home).
Coturnix are domesticated, typically the easiest species to look after. They are relatively cold hardy, and do well as long as you keep the wind and rain/snow off of them. They don't come in different breeds, but they do come in different color morphs (e.g. Pharaoh, Golden, Texas A&M).
Coturnix need the least space of all the commonly kept quail (1 square foot per bird), but will appreciate and use more room if you give it to them. You can keep them in pens on the ground or on a deep litter substrate (or on wire, raised off the ground).
You should keep at least three birds, so the flock isn't destroyed if one bird dies. You can keep all males or all females, or keep both sexes together (with a ratio of at least 3 hens to 1 roo) if you intend to breed them. Keep in mind that if you have more than one roo, you may experience fighting.
Quail are very easy and rewarding to raise. My birds all have distinct personalities and habits, and it's a joy just to watch them. They eat out of my hand and let me pet them while they dust-bathe. Some are more nervous than others, but even my dog can't truly scare them. If you want a pet bird that's beautiful, relatively tame, and lays eggs almost all spring and summer, Coturnix are a good choice.