I've never worked with a bank that tried so hard to keep me from my money.
I hailed from Europe to USA in 2003. Got SSN, went to first Bank of America branch and opened account with $100 initial deposit. No problems at all. Credit Card was tricky - yes many banks will tell you "bad credit is better than none", but after 60 days of direct wire from my employer to the Bank, they gave me secured $500 Amex. That was enough to show them for the next 60 days I used it and paid on time. Within 3 month from getting SSN and my first banking and working legally full time W2, I already got "you are preapproved for credit card" letters in my mailbox.
2 years later I opened Business Account with Bank of America and never had problems with them since then (online sales-related business). Not to say they are perfect, as BOA was known to claim they own properties (by mistake) and being stubborn in courts even if they knew they are wrong.
The only reason I'm resultant from switching to something smaller is the number of ATMs available; otherwise my choice would bt BB&T.
on most banks the offer letter will already give you a $500 credit.
years ago, they were the only bank to open an account with my history from another country. all other us banks had the same bullshit "you won't even have a credit card with us until you have credit history in the us, even though we have branches in the country you have history".
then they were the only ones offering investments with no administration fee and with returns above the monopoly of .5 point under official inflation. they were actually 1 point above.
but yeah, every time I travel and forget to tell them before, my card get lots locked. and they claim they didn't call me before locking because it was sleep hours in my home timezone, in case I wasn't really traveling.
also driving in the us, every time I stop in a motel 6 and such, locked card.