Logo file size for multiple uses in web app

The web app I work on currently has users upload different logo files for each product use--favicon, site logo, print logo, etc. We want to change this so users upload one file that can be used in all cases. I don't have a strong graphic design or visual design background and am struggling to figure out what size file we should ask users to upload for all these uses. My internet searches have only turned up best dimensions for specific use cases.