No, I don't think Tucker Milling is a bad brand. I use TM Gamebird feed for my Quail and currently use the Flock 22 for my adult chickens. The Flock 22 is a pellet so it would be hard for small chicks to eat.
For tiny chicks within a mixed flock of adults, I'd feed either a chick starter or an All Flock feed to everyone. Just provide oyster shell free choice, the hens will take what they need.
Purina has an All Flock that I have used off and on for years, it seemed to be o.k., but my TSC went way up on $$$ and the feed they were getting in wasn't very fresh. So...I switched to a local Mom/Pop feed store which carries different brands like Tucker Milling, Blue Seal, etc. Never used Kalmbach, but it's not something I can get here "local" but I've seen quite a few posts mentioning it and people seemed satisfied with it.
As for chicks and Coccidiosis. Some do feed a medicated starter and if you feel you may have problems then it may be something you need to feed - do keep in mind the amount of Amprolium in the feed is minute, so it will not treat Coccidiosis. Chicks need exposure to poop and soil in which they will live to help build resistance.
So, basically, keep some Corid on hand.