Does Breed Count matter when considering a starter team?

Breed Count the number of times the axie has been bred. Each axie can be bred up to 7 times. If you’re aiming to breed an axie in the future, you can choose a 0 or low breed count axie. The downside for this is that 0 breed count axies are pricier.

If you just want to use said axie as a starter or for full combat, it's safe to choose higher breed count axies since they're usually cheaper and there's no bearing in combat anyway.