So.... how much does it cost to be a strong magician?

Well, bishops are generally richer than archmages because they spend pretty much nothing to train 1-120, and most of them regularly attend zakum or horntail runs for profit. Their ultimate also costs less, and they can let other people leech better for more money.

Also, what's your definition of strong? If you're talking about stronger than the average magician, then the equipment you listed will definitely be way over the top. For example, I doubt more than 50% of magicians have a successfully scrolled zakum helm, 20/12 earrings, or an elemental wand. And how is it harder for an archmage to get into a horntail run as a buyer as compared to any other class? Buyers just stand outside anyways.