I use CalDav for calendar, contacts and tasks sync and share with the rest of the family.
Server is Nextcloud with WebDav/WebCal/CardDav and DavX5, Etar calendar, native contacts and OpenTasks on android. On Linux WebDav to access and sync Nextcloud files.
How do you use them?
Edit: Added CardDav for contacts.
I think Nextcloud is an easy option. Lots og dedicated WebDav servers out there. For CardDav and CalDav (Contacts and calendar) I rembember that Radicale is a good bet: https://radicale.org/v3.html
Radicale is more specific, it is CalDAV/CardDAV and not WebDAV. If that’s what you’re looking for, it’s an amazing option. I’ve used it for years and I really like how it stores calendar events as a folder of ICS files; it makes backup and sync very easy.
For a general, lightweight WebDAV server, you can use the nginx DAV module. Nextcloud (or whatever you use) probably will be reverse proxied by nginx anyway, so if you can just enable a module in nginx, that’s pretty much as lightweight as it can get.
edit: forgot the link https://nginx.org/en/docs/http/ngx_http_dav_module.html