We are very lucky with our bank, as its online facility has a lot of features, and the staff are really helpful when we ring them up. Our bank has very few branches, so most of the customers rely upon the online facilities, so they have to be good for them to stay in business. Our nearest branch would be about 700km away.
We move our money around by logging online and using the interface. You can create as many accounts as you like, and can set up automatic movement at any period (for instance 1st day of the month, weekly...) from one account to another, or externally. So when money comes in, it can automatically be diverted to the appropriate accounts. In Australia, most companies can be paid with BPay or direct deposit (or direct debit, where they pull the money from your account), which can be set up automatically with our bank accounts. All of our periodic payments, including paying the credit card in full each month, are done using this. Whenever we get a bill, we just log on, say what day we will send the money to them, and it is done.
If we get a cheque (once a year), we can take it to the local post office to deposit it, but cheques in Australia are quite rare now, and the banks were talking about phasing them out. That hasn't happened because there are places with no credit card facilities (no internet or phone connection) where cheques are used.
It is really simple to use, and we can even name our individual accounts, so they can be used like the envelope system - but automated!