It helps to think of easyJet as a completely new flight starting in London. Be sure to read all the regulations on their website; they are enforced. The airline lets you check in on-line many days in advance. That's when you buy such "extras" as checked luggage space and seat assignment. Be wary of luggage rules that may not match BA trans-Atlantic. The basic fare allows one carry-on item. That's ONE, not a bag and a purse and a computer. Want more; pay more for the seat. And do it in advance because transactions at check-in are more expensive.
When you get your checked bag from BA you may have to take it to an easyJet counter outside the secure area (I'm not sure about this). That will mean going through the British immigration process. Access to the plane itself will probably be crowded and may involve walking on the tarmac, but it will be quick because all budget airlines need to turn around their planes and get them back in the air fast.
You should have plenty of time to make the transfer, but always keep it in the back of your mind that if your first flight is delayed enough to miss the second you will get no refund nor replacement from easyJet.
Also, budget airlines are more prone to schedule changes than the transcontinental carriers so keep an eye on your reservation as you proceed to next year.