The most important privacy consideration is who gets to see this data. If you just use it internally and not share it with 3rd parties, then you are already ahe

The most important privacy consideration is who gets to see this data. If you just use it internally and not share it with 3rd parties, then you are already ahead 99% of the businesses in terms of privacy. To keep the data for yourself, it's best to use a self-hosted analytics platform. Most of them also allow for more granular settings, where you can set exactly which data is stored and how.