If the line is to serve central Warrington there will need to be either a tunnel or viaduct to thread the town, the old Bank Quay Low Level route is too twisty.
The old alignment across the Mersey through Lymm is compromised by development and the M6, and all the approaches to Warrington have dense modern residential areas to avoid.
The area through Rixton east of the M6/south of the CLC is pretty empty (it used to be a mix of bog, "night soil" deposits and canal dredgings), but reaching there from Penketh will be expensive.
And an M56 route takes you well south of Warrington centre (though still within the modern borough, eg Stretton).
Either way you need a new viaduct over the Mersey unless you use the HS2 one on the Golborne branch around Warburton.