Your first Amex in UK should either be Platinum Cashback, Marriott/BA Avios or Platinum Metal card.
If you get Rewards or Gold Credit Card as your first amex card, you can't avail welcome membership reward points benefit on platinum metal card till next 24 months. Also, you won't be able to avail any welcome benefit on Gold Credit card/Rewards card for next 24 months if you get any Amex whether it's Cashback/Marriott/Vitality or BA Avios card (and vice-versa).
One more thing.. Amex doesn't offer charge cards in UK and both Gold & Platinum cards are now credit cards.
In terms of value back, only three cards from Amex UK make sense.. Platinum Metal, Gold Rewards and Avios. If you want a basic card and you're happy with 0.5 to 1% cashback after 3 month promotional period, go for Amex Platinum Everyday Cashback card (free) or Cashback card (25 GBP annual fee).
You'll need a UK bank account and address proof (bank statement would do) on your father's name. Wise won't work and any mainstream bank including Monzo will be fine.