Nearly all (if not all) personal online banking is free, there are no charges to set up, no charges for money transfers etc. When setting up your online banking with your bank its always worth making sure its 100% free online banking (just in case).
The only times that online banking might not be free for setting up or transactions is if you are setting up online banking for an offshore account, an international bank account or a business bank account.
If you find a large bank that charges for any aspect of its online banking then please let us know.