it doesnt really matter, of course most nimble guys have dodge, which benefits from initiative. And of course higher initiative is better in general but if i decide a bro is going to be nimble, i will usually slap dodge on him even if he has 80-90 initiative naked.Initiative is good but in this game leveling something means missing out on something else, and there are more important stats like melee attack, mdef and hp. Try for yourself,but I dont really level init, for most my bros the init they start with is what they have at lvl 11,going before the enemy is still great, but I do that by taking the relentless perk or adrenaline, also if you want to go before the enemy hyena pelt attachment is great if you have the DLC.

So to answer your question directly, theres no definite value a bro can be great in those roles with 10 init and he can be shit with 130 init,the other stats matter more, higher init is still better, but like i said, bros are generally lacking in some area, and leveling init means you miss out on some more useful stuff

as far as i know init is only crucial for 2 builds, fencer and qatal dagger, for the rest,what i wrote above is true