How do I go about breeding chocobos?

[Torvald]

You don't have to start again from P1 unless you threw out all your fledgling registration forms. Raising and breeding one of the 10 fledglings, even if it's not perfect stats, would be much preferable to starting over from P1.

A strategy that warked (!) for me was just to spend extra money each generation on finding a cover with decent stats. I averaged about 8-10 covers per generation before finding one that I liked.

I really liked this quote by Momomi Momi.

When starting out, a successful covering is one that introduces 4 star stats into the gene pool. Anything else ultimately doesn't matter. The eventual (middle) goal is to introduce 4 star genes for all stats. And then you want to get "guaranteed" 4 stars, where both the mother and father pass on 4 star stats.

At P4 you still have a long way to go, and having 3 '4' stats already is way ahead of schedule, I think. You're doing great and keep it up!