If a website has 100 pages and you wish to learn from a survey which are the most important or useful to people, what percentage of the 100 pages should you ask people to choose?
Should you constrain them to five answers or allow them to choose (up to) twenty? Would the need to analyse four or five user segments affect the answer?
What are the statistical reasons?
From the phrasing of your question it sounds like you are looking for a quantitative solution ("what percentage of the 100 pages" and "constrain them to five answers"). It is really hard to design surveys properly. You need to ask the right questions to the right people. You need to be aware of self-selection of participants, and how this may impact your site's target demographic. There are lots of issues, and books have been written about this topic.
What I would suggest, as a start, is to not worry about statistics too much. Rather opt for a more qualitative approach, and ask people two simple questions:
What is the best part of the site?
Name one thing that you think this site is missing at the moment.
The first question will allow people to list things they like, in any order they like. If you aggregate all the results, it should (hopefully) align with your analytics data.
The second question will do three things:
Show you what people think they want from your site, but limit them to be very specific. If they could only list one thing, they will most likely list the most important thing to them. This is valuable information.
Highlight which portions of the site are actually useful, but there are people who do not know that it exist or where to find it (assuming they name something that already forms part of your site)
Provide you with a starting point from which to prioritize your redevelopment efforts.
Maybe people don't have a problem with your site. Maybe they actually want a better mobile version or app (as a hypothetical example). If you ask 100 people, and five say they want a mobile app, is it enough? That is a decision for your management team. But still, you would not have known about this apparent need in a structured "list your top 20 pages" style questionnaire format.
Unless your website has a statically insignificant number of visitors, I would prefer the results of tracking your website via Google Analytics over any survey.
Surveys inherently posses a multitude of problems, foremost low completion rate and high dependence of result based on order of questions, question wording etc.
Use real-life tests of your pages with users for a general idea by observing their natural behavior and comments. You can then build upon that basis with using metrics from Google Analytics.
This article by Leisa Reichelt explains that confidence in decisions is more important than proof and suggests ways of improving understanding:
If you are doing qualitative design research, don’t worry about sample size. Sample size and statistical significance don’t matter.
The only thing that matters is how confident your team is about the next decision they need to make.
As the site exists with so many pages, you can also consider incorporating the survey into the site itself.
For example:
At the bottom of every Microsoft Support page, there is a question on the page that says "Was this page helpful?"
You are basically qualifying the value of each page.
