How many hours it takes?

Specifically, links that buff damage are
Hayato: +10 all-stats, 5 atk/matk (level 70)
Cannoneer: +15/25/35 all stats, 5/10/15% hp/mp (level 70/120/210)
Demon Slayer: 10/15/20% boss damage
Demon Avenger: 5/10/15% total damage
Phantom: 10/15/20% crit rate
Luminous: 10/15/20% ignore pdr
Mercedes: 10/15/20% exp gain
Xenon: 5/10% all stats (70/120)
Kanna: 5/10% total damage

If you're starting from 0, I'd probably prefer Demon Avenger, Xenon, Kanna, Mercedes. Any of those will make future characters quicker.

As for character cards, the more level 100+ chars the better, that's about it really. Until you have 3 sets of S cards don't worry about specific classes.

Mikhail can affect exp gain in early levels, but it isn't worth prioritizing unless you intend to use it for your main class and it is useable by it. Angelic buster isn't bad, either, though it's probably the slowest of the new classes to train.