There are so many types of online bank accounts it can get overwhelming. Savings, investment, or current accounts, nowadays you can open most of them easily and manage them from the comfort of your home. I think that last part is what I like best about online banking, not having to go to the bank. I live in the middle of nowhere, and the next bank is about half an hour away. As all the people who live in the middle of nowhere seem to have banking needs at the very same time, there are often long queues and being able to manage simple operations from the computer is amazing.
When you look at basic bank accounts, the offer is generally very similar between all the online banks. A small overdraft, a free withdrawal card, and zero fees are the norm. If you do your research a little more, you should be able to find an account that really fits your other banking needs. For example, I have an account that gives me cash back on my common expenses. It comes with a small monthly fee that is more than compensated by the cash back I receive on my utility bills (something I know I will have to pay every month anyway). It also has a credit card with no cash withdrawal fees abroad, which is a feature I used to pay a lot of money for in the past as I travel so much.
Those two things work perfectly for me, and they will not fit most of the households. As I do not like to have a lot of cash on my account, I generally don’t look too much at the savings rate the online account offers. But if you keep 6 months of living expenses in cash as an emergency fund, you may want to have a closer look at the interest rate offered by your account. $10,000 at 3% per year is $300 in interest, it is only $50 at 0.5%, a rate most high street banks are offering those days.
Also look for the fees of the services you use the most. If you are often overdrawn, choose the account with the lowest interest rate, or the lowest charge on bounced cheques. They may not have nice perks like other accounts but if you are going to need an overdraft, you want it to be as cheap as possible. I used to have an account with free travel insurance. It was great because once again, I was often abroad. But when the cash back account came out, it made more sense to get cash back than to get the travel insurance, as I was now living less nomadically. Some online consumer sites can help you see all the features of online bank accounts in one page and save you a lot of time to make sure the account you choose it the right for you.