What qualities you select for in your breeders depends on what you like in a chicken, and what you feel needs improvement in your current flock. Since you're not going to be breeding to a specific breed Standard, you can select for whatever is important to you -- health, vigor, longevity, foraging success, friendly temperament, broodiness, lack of broodiness, egg production, rapid growth to slaughter weight, slow growth to slaughter weight but retention of tenderness, breeding behavior, fertility, feathering quality, survival instinct, etc,etc. The list is literally endless.
Be aware, however, that you can only focus on so many things at once, and while concentrating on one thing you may lose other things that you like. If you want to focus closely on multiple things, you might be more successful having multiple breeding lines, each dedicated to being superior at one thing, plus have your "middle of the road" main line. Then occasionally, infuse some of your focused genetics into your main line in hopes that it takes up that trait more strongly. Always be careful of extremes in any characteristic. They usually come at a high cost to other characteristics.
Also be aware that the breeding results you get in the offspring of hybrids is quite unpredictable compared to non-hybrids., even poor quality non-hybrids. With non-hybrids, breeding a red bird to a red bird usually results in a red bird. In hybrids, breeding a red bird to a red bird may give you a huge array of colors, depending on what genetics went into making the hybrid red over several generations. The same principle applies to all characteristics of the animal, not just color. We like to think that breeding a small bird to a large bird will give us a medium bird. That's logical, but doesn't happen as often with hybrids as with non-hybrids. That's not necessarily a bad thing, but it can be quite a surprise if you're not expecting it, and a big frustration if you have a specific breeding goal.
