For the most part all you'll need is your US passport.
My personal assumption is that the border officer wants to satisfy themselves that one is property entering the country for their stated purpose. I figure that is usually achieved with the questions that I've been asked -- "What is your purpose for entering the UK?" "How long do you plan to stay?" And "Where are you going when you leave the UK?"
If there are any doubts on the part of the officer, assume that you'll have to show that you actually intend to leave the UK and that you can afford to take care of yourself while in the UK. Figure that for most folks proof of onward travel is all that is necessary and sufficient.
Personally except for a few confirmations and vouchers I am not carrying much in the way of paper. But I insure that on my phone I can prove my reason for entry, my onward travel and that I have ties at home (employment and longevity, family, etc.), and that I can afford my trip.
I am able to do that through my travel apps -- United & Amtrak, plus UK train and ferry operators I'm using. As a state government employee, necessary employment information can be accessed through a portal. And well banking is through an app as well.
You're not going to need to carry some giant binder full of papers and documents -- your US passport is sufficient, and it's all I've needed. But it does not hurt to think about how you can provide necessary information to satisfy border officers for entry.