Check with Go-Compare-the-Meerkat's Money-Supermarket for what each bank offers. Only you know what is a valuable perk to you.
Google 'who owns which bank' or similar to check which bank holds the banking licence. Choose separate banks, not just separate brands (fascias) operating under the same banking licence. Just for added security.
Check for customer feedback ratings - if you believe that sort of thing. For Example:
www.which.co.uk/money/banking/bank-accounts/best-and-worst-banks-a3q5d8c6dj7y
We have one with Nationwide. Pay a fee but get car breakdown, travel insurance, phone insurance etc. Nothing gets paid out from that account, it just sits there with the minimum amount in it. Lost interest plus fee is much less than we can get equivalent cover elsewhere.
We have another which pays 5% interest but only on a very small maximum amount. That is linked to PayPal and Amazon accounts to limit our potential fraud losses. Nothing else gets paid from that account.
Main one is with Santander. Pay a fee but get cashback on utility bills which just about pays the fee. Gets a little interest. All the big standing orders, credit cards etc get paid from that one. Not as good a deal as it was when first launched, but still better than a basic savings account.
We still have our original ones with Lloyds, but I can't recall why. I never use that one.
I only carry the cash card from the Santander account so that I don't accidentally draw my pocket money from the wrong account. My wife carries all of them - see below!
Visa, MasterCard and Amex credit cards for similar reasons, chosen for cashback, zero fees or whatever is most useful to you. My problem is remembering which one I'm supposed to use for what to maximise cash-back, store vouchers, air miles etc, so I'm down to carrying only one Visa and one MasterCard. As I'm now retired I can't recall when I last used the AMEX one.
Most bank accounts require a minimum balance and/or minimum amount paid in. We set up a standing order from the bank my pension goes into to pay most of it to the next account in the chain a few days after it comes in. A standing order transfers all of it from account 2 to account 3 in the chain the day after it comes in. The chain continues until it gets back to the first bank and then the Direct Debits get paid out. Takes a while to set up, but once done is automatic. Currently the bank's systems are too dumb to differentiate between salary/pension going into an account and other standing orders coming in regularly.
Only works if you have them all on-line and are reasonably diligent in managing your cash-flow and paying credit card, PayPal, Amazon etc by on-line transfer from the right account(s) at the appropriate time.
I don't have the patience to battle through the layers of passwords and memorable data, but my wife revels in that stuff so it has become added to managing the birthday/Christmas card list as yet another piece of 'wife-work' in our household. She spends one afternoon per month on it. Worryingly she can remember all the passwords, security checks, memorable data with total accuracy for all the accounts. I cannot guarantee first time access to my own accounts even with a crib sheet.
Is there a sofa I can hide behind at this point?