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It is simple. Form a Ltd in the UK, you need a Director and Company Secretary, both can be US residents operating from a US address.
>2) Corporation or LLC type entities;
In the UK the most common type of company is a Limited Company (Ltd). The UK has two primary types of company "Limited" (Ltd) and "Public" (PLC), given you are not floating on the stock exchange, Limited is the one for you.
>3) any other information that may be helpful.
Set up a mailing/registered office address for your new UK company, which I assume the management will primarily operate from the USA? There are many services that will create bank accounts for you, provide you with UK "virtual offices", mail forwarding, telephone forwarding, office facilities, you choose the most appropriate services.
I'm British, reside in the USA, run a UK company via a "Virtual UK Office" from the USA. My UK mail takes 5 days to arrive in the USA via my "Virtual Office", faster than some of my USA mail. Phone calls can be answered immediately or redirected as I wish.
For all reasonable purposes operating a UK company is no more difficult than operating a company in any other State than the one you choose to reside in. Simply think of the UK as the 51st State of the USA with a few odd rules and you will do just fine :)