Based on my experience, easyJet are fairly strict about carry-on size, but that seems to depend on which airport you're dealing with. I've found that my carry-on is not always checked in the sizer, although one should be prepared for that. Weight is not a concern, as long as the passenger can lift their own luggage into the bins (the flight attendants won't be doing that for you). I believe they include the wheels and handle in the measurement (one reason I don't use wheelie bags).
The main item to be aware of when buying the cheapest tickets with easyJet is that they only allow one carry-on item per passenger. That doesn't mean "one plus a personal item", it means ONE ONLY of the approved size.
If you decide to check one bag, you should easily be able to arrange that using the "Manage My Booking" page. I always check one bag and also pay for the next highest weight tier at the time I make the booking to ensure I won't be over the limit, as it's considerably more expensive if they find a checked bag overweight at the airport.
As you may have noted, you can check in and print your boarding pass up to 30 days prior to the flights. There is usually NO check in at airports, but only a bag drop. I usually pay for speedy boarding and seat selection.