This is a tough question. It's been a decade since I looked at specifics, but there can never be a "one size fits all" answer. For that reason, regulators will be reluctant to offer guidance. There are many factors to consider and you have to look at it the same way you judge the need to retain every type of paper-based record for every product or service you offer.
Depending on the content of your site, many different federal regs can apply. Each reg will have its own record retention rules. Your state(s) might have laws and rules requiring retention of certain items, but in all cases, state law governs contracts. In disputes about contracts, you may find it necessary to present evidence of not only a copy of the contract or service agreement, but also the pre-consummation representations.
There may be better products site capture today, but the full commercial version of Adobe Acrobat used to be the cheapest and easiest way to capture some types of websites. Static pages were captured with almost every feature functioning as it did online. Sites that generate pages from databases on the fly are the toughest. Fortunately, the systems that house the DBs should have their own backup & retention capability.
The worst possible way to capture and retain website content is printed paper.
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...gone fishing.