I switched from a local bank to Schwab about 8 months ago.
Your top concern was my top concern too, and so far it is working for me. I find I do very few deposits to an account, as my payroll goes direct. A few checks a month mailed in seemed like it might be a burden, but so far i am happy. Schab gives you all the pre-addresses and paid envelopes you want. I used to drive around with deposits till it was convenient to go to the bank. Now I just have to wait a few days for the deposits to go through.
I don't use a lot of cash, but from time to time I want to draw $1000 in cash, and with Schwab you can't do that, or at least I haven't tried hard enough to find out how.
I go the the ATM 2 days in a row, now, although that is a hastle and only being able to get 20's is a hastle, but I get over it once I see my statement and enjoy the interest and completely free ATM's anywhere.
Your call, but I am happy. I do use the Schwab one account and have built up some Money market savings which gets even better interest than the checking account. And you can move it back and forth no cost!