Something to know about going to a bank in person...
When you go to the bank in person, the teller essentially logs into online banking for you. Then they scan any checks you give them and deposit the scans to your online account. They withdraw any money from your account online and give it to you.
You aren't changing much by having them do it instead of doing it yourself, except that they generally have a direct connection over a private network, instead of going over the internet. When you do it yourself, it goes over the internet using SSL encryption, which should be very secure. As implied in this thread, you do need to make sure your local network is secure, and probably avoid doing banking over public Wifi, such as at a coffee shop.