I think one of the obvious solutions is to run the soccerbus service from Old Hall Street. I can't stress enough how this station is gonna heave with Blues. It's served directly from Chester, Ellesmere Port, West Kirby, New Brighton, Southport, Ormskirk, South Liverpool, and Kirkby, is less than 1.5 miles from the ground, and just happens to be in the city centre.
And then there's Sandhills.
I understand that not everybody has convenient rail access, and perhaps ironically, it will be people who live close to Goodison, and other such areas who will find it hardest to get there. Their journey will likely start with a bus into town, but for many people who rely on public transport in those areas, a two-leg journey via town is par for the course.
I think the rail links are fine. Certainly better than Goodison or Anfield.