Hotels are always really expensive when Liverpool are at home due to tourists but usually less so for Everton. Having said that weekends can be expensive as it’s quite popular for a night out. If you are looking for cheap hotels in the city centre that are OK try Tune Hotel or Printworks...
From New Brighton you can get the Merseyrail train to Sandhills (via Moorfields) and get the Soccerbus to the ground. Look on Merseytravel website for more info.
I’ll probably be doing the same from Moorfields as I have a season ticket in a nearby car park.