A redesign that changes fifty things at once cannot tell you which of them helped.
Looking dated" is rarely the actual problem, and a redesign undertaken for that reason usually does not move the numbers.
Changing everything simultaneously makes the result unattributable, which is why redesigns are so often followed by disagreement.
Diagnose first — the funnel, by device, tells you which two or three pages are actually losing money.
Keep URLs, structured data, heading hierarchy and internal links intact, or you will trade design for traffic.
Look at the funnel by device before looking at the design. If people arrive and leave from one specific step, that step is the problem and fixing it is far cheaper than a redesign.
The full guide has the formats, the deadlines and the worked examples.