Unless things have changed recently you do not need exclusively PCR tests, lateral flow is acceptable which are cheaper, easier and quicker. Just for future reference.
Travel to USA for USC's require:- A negative PCR or lateral flow test result within 3 days of travel for passengers 2 years old or over
Travel to UK requires:- A negative PCR or lateral flow test result within 3 days of travel for passengers 5 years old or older
- Pre-booked Day 2 & Day 8 tests with an approved provider for passengers 5 years old or older
- Passenger Locator Form(s)
So travelling to the US is pretty pain-free comparing it to the UK. I don't know your circumstances but ensure you have a plan for your test-taking to come back to the UK. It's the same as travelling to the US, you will be denied boarding without them.
I recommend Qured. They are cheap, approved and post the tests to you for you to take abroad with you. You then do the test via video call and then you send them a picture of your test and your passport and they send you a certificate (providing it's negative, of course). Very versatile.
So, to answer your original question this is all you need. Having recently travelled to the US I recommend you print your covid test results if possible. You get asked constantly for them at various stages. The same with travelling back but also include printing your passenger locator form(s). I'm happy we did this as my wife's for some reason wasn't coming through the UK border system but we printed it out and it solved it all in seconds rather than 15 minutes.
Just a note: I don't know who you're travelling with but American Airlines require masks to be worn on their flights. It's worth taking a few masks for all of you with you in case you drop them etc etc.
All this is as of the requirements today!