Watched both this year from multiple locations, and did Liverpool year before, Chester looked a lot of fun, good PB course, not sure about crowds. Liverpool definitely improved their course from last year from results, lots knocked time off so equally good for PBs now, and more crowds watching.
Liverpool is easier to get around for your wife and kids during the race, they can nip on the train from Wirral to town to see you 2-4 times and more crowds, better views of city, plus finish along the seafront to Liver building is spectacular.
Both well organised races. Take your pick.
any first marathon will be special of course, best to give yourself as long a time as possible to train upto it, so would hesitate about Edinburgh unless you're running consistently now. It's a good course though.