The ACH model is fundamentally insecure: anyone who knows your account number can pull money from it, and the protocol makes no allowance for the bank to check with you first. I don't think choice of bank matters very much.

You can manage your risk somewhat by:

1) Using credit and not debit cards for day to day spending.

2) Maintaining your long term wealth in separate accounts at separate institutions and not linking them directly to anything except your checking account. This minimizes what can be stolen if your checking account is compromised, and makes it less likely that your savings can be stolen directly (account number is used in fewer places).

3) Turning on all the alerting and notification settings you can find, so that you'll hear about unauthorized activity immediately.