Some Amex cards are indeed the best for cashback - but it's such a faff when you find a retailer than doesn't accept them. I'd rather get slightly less with a Visa or Mastercard that you know is accepted everywhere.
AMEX generally has the best deals on cashback with the credit cards or points with the charge cards. Can always have a fee free visa or master card that collects points under some other scheme for other purchases.
Never had an AMEX card, never been a fan of having to pay to upkeep a CC. I always just go with free ones.
The platinum credit card is cheap enough (£25) and offers a good cashback deal.
The Gold charge card can usually be had for free for the first year, usually some offer where you get bonus points if you spend X amount in the first 3 months, you get a couple of lounge passes too, can just cancel at the end of the year.
The following year perhaps get say the BA AMEX card (there is an annual fee if you go with the premium charge card option here though it does have a very, very sweet offer in the form of the companion voucher for a flight).
There is some time limit before you can sign up for another gold card and get a free year and points deal but you can cycle these cards a bit... like get the BA one year when you're planning a big holiday and fancy using your points etc.. get the gold card the next then the platinum credit card the next etc..
Black card - Invitation only.
^^^ that one used to attract the posers/Essex wide boy types etc. a few years back you'd get self-employed people putting as many business purchases through their platinum card as possible to get the 100k or so spending requirement... I think they've wisened up to that now and have ramped up the requirements + the annual fee.
There are still the consultants/salesmen/account manager types who manage to slip through the net though, unlike the self-employed wide boy types who are easily rumbled these guys do travel a lot and entertain clients etc.. and so are putting through exactly the sort of spending AMEX looks favorably on... only they're not actually paying for it but submitting expenses to their company. It used to wind up the travel secretary at one place I worked at, it's her job to book flights/hotels but some guys would insist on doing it themselves and if they're putting through last-minute business class tickets regularly + good hotels etc.. then their spending can be pretty high.
The slightly sadder thing is the highstreet banks copying it - you can get a "NatWest" or whatever "black card" now... which just seems a bit too try hard.