Best Bank Account for ....

I get interest from Natwest - but minimal (0.0?%)?
Lloyds has strict conditions for the 3% - best used as a savings account where you can more easily control the conditions.
First Direct? - can you pay in locally? I don't know.
Santander - Can't comment on the customer Service but the new 123 account looks attractive if you keep £3K plus in it (3% plus cashback - which outwieghs the monthly fee)

If you are able to manage your money, it might be worth considering more than one current account. Most of the banks have something attractive to offer, but probably none of them offers you everything that you ideally would like. Of course, you can compromise - or you can consider what I am doing: cherry-picking, by using several accounts.

I am very happy with my Santander 1-2-3, which I opened mainly for the cashback and the great interest they pay up on up to 20K balances. Online interface quite good. FP limit is £100K/day but they block your online access if you are making larger payments and they cannot get hold of you on the phone to confirm you made the payment.

Also got a Nationwide Flexaccount - - it pays no interest at all but the online facilities are excellent. I have that one so I can get their Flexclusive ISA. Other savings accounts are uninteresting, apart may be the MySave Plus one, if you can lock your money away for some time. Not sure about their FP limit. Oh, and the Travel Insurance that comes with the Flexaccount is actually quite good.

Lloyds - - got some Vantage accounts because they are still paying 3% (ish). Their online interface is very good. Used to have some savings accounts there, too, but their rates are no longer attractive enough for me. Sometimes getting bothered with requests to visit Branch, where they are trying to sell me something I don't want. FP limit 25K/day.

First Direct - I have this account mainly so I can get at their Regular Saver account. They pay no in credit interest, and apart from the Regular Saver, their savings accounts are pants. As already mentioned, the online interface is getting a bit dated, but I have not had any problems doing what I needed to do. Not sure about their FP limit but never had any payment stopped by them. You can use HSBC branches for over-the-counter business (paying in cheques, withdrawing large amount cash).
I think you can still get £100 for opening a First Direct account.

Then I have some Halifax accounts, for the £5/month they pay you if you pay in £1K each month. They also used to have some good savings accounts but have slacked a bit recently on that front. And still got my OneAccount going as well, even though it is in credit. Just nice to know I could get at a large sum of money at decent interest and without any notice.

Natwest have a very easy to use online interface but they were never very good with interest, on anything. Similar is true for Barclays.