Quite often you might receive a report of an accessibility audit done by another company. Usually, the auditor provides information about which of the issues are most problematic - either they are more common or they affect crucial parts of the website. If you get such a report, it's quite easy to define what to fix first. But for the cases that don't provide you with any info, here are some quick tips on how to get started on the fixing process.
Start by reading through the report to see all the problems they've discovered. Most often the audit is not done of the whole site, so check what has been tested. If there are unclear wordings in the report, make sure to ask the auditor for clarifications as soon as possible.
When you have a grasp of the issues, think of the website as a whole - do some of the problems reported affect a crucial part of the site's functionality? Those kinds of issues should be fixed first, regardless of if they affect only a single page or the whole site. A few examples of these kinds of issues might be problems with a shopping cart, problems with forms on the website, or problems with the site search. All of these have usually a big impact on the site's users.
The remaining issues can be either fixed by the order of impactfulness or by the order of how easy they are to fix. If you know you can fix, for example, some color contrast issues in a few minutes, even though they might be less impactful than some other problems, it might still be a good idea to get those fixed quickly. Then those are out of the way and you can focus on the rest.
And since all the issues reported need to be added to the accessibility statement of the site, fixing the smaller issues will show the site users that there is progress.
If there is a client involved, they might want to have a say in the order issues are fixed. Make sure to get their comments on your plans. In my experience, the client usually trusts my thoughts on how and when the issues should be fixed, but it's still always nice to present my thoughts to them. They know their site the best and they will often have really good insight into which page is the most used by their users, which I might not have.