Qualifying Credit Card

So i have a friend looking for a credit card to build credit. His goal is to be able to purchase a house. He currently has a score around 620. He does have one credit card in good stance, he does have a collection from while ago, (he was at 400 at that time) and he makes a decent amount.($500 a week)
My question is, i currently have a friend who works for an asian bank. She tells me i can try with them. Would he be able to qualify for it more than say Bank of America or chase?

He wonders if he should try out BoA first, if failed, then the asian bank. but if they deny him at boa, it would lower his score and perhaps the asian bank.

What should he do? Im thinkin just go straight to the asian bank and try his luck there.