>>64361 (OP)
Sounds pretty cool. I don't know to much about them, but flipping through wikipedia and http://bestiary.ca/beasts/beast265.htm gives me a lot of ideas.
But to answer your first question, I would say to not worry about what's "good" and focus on what you want, and then make that judgment later when you've got something to evaluate.
If it were me making this character, I'd decide on a body type and overall size first, then focus on unique physical traits and a color palette. For example, that SMT cockatrice is great. It's mostly four colors and the comb and the thing on the throat are very striking, along with the blue scaly underbelly and legs. It's easily identifiable as a cockatrice without looking like a lizard with a rooster head i.e. a generic cockatrice.
As for the images I attached, these are just some things I found interesting that might help you. The first pic isn't particularly what you're looking for, but I found the head to be well done. Don't ask me why it has a snake tail, as the picture was tagged cockatrice and not chimera. I guess they didn't know the difference.
Number two is DnD's interpretation if you don't want to stick with mythological source material. Plus, the bat wings and rooster torso look really cool together. Third pic is just rad, add a few reptilian features most of them would probably be under the robe, but still and swap the heron head for a rooster's head and it'd look fantastic.
For bonus points, try to visually incorporate scales and feathers on your character. I've got a few examples I'll post next, but it's something that'd definitely set your character apart from the rest.