I flew into Manchester Airport which is about 45 minutes away from Liverpool (on Delta. St. Louis to Atlanta to Manchester and the reverse home). I didn't check the cost of flying into London and then getting a train. I do know there is an Atlanta to Manchester flight that gets you there first thing in the morning every day (or there was 3 years ago). For us Americans, landing at an airport 45 minutes away is fairly normal. In England it's in a different city. So I doubt finding a flight to JLA would be cheaper.
I looked at hotels but found a great deal on AirBNB at a flat in the Seel Street neighborhood, which is fantastic. Lots of bars, restaurants within blocks. It's also easy walking distance to the Lime Street station, where can get a train to the Kirkdale station which is about a 10-15 minute walk to Goodison.
My cost was different because I have a buddy who is a pilot for Delta so I paid $500 for round trip, and one of the lads on here got me a comped ticket.