The main advantage is that credit unions are member-owned and therefore run to benefit the members, not some investors. This keeps them from having an interest in screwing you via weird fees and whatnot. The main disadvantage I've seen is that smaller ones have less leverage and so you pay more ATM fees to other banks.
I've been in the no credit card boat, so I know exactly what you mean. I got mine by having a car loan I don't really need that my brother cosigned to create a credit history. You may also be able to get a loan from your broker. Mine keeps telling me how big a loan I'm approved for, though I've never tried it.