If it was a public site for any user, I wouldn't offer just one because a single wrong choice could alienate the users you want to use the site. It's common to have a few such as Facebook, Google, Microsoft, and/or Twitter. If it was an enterprise site where the people in your company had to log in, I would use something as close to the technology stack I was using as possible. I'm thinking about something like Google or Microsoft, especially if you were using a specific workspace (email/docs/etc.) solution that was standard for the company.
If it's work related, Google. But I generally don't use any of my personal social accounts for logging in to anything.
I wouldn't. I never understood why localshop.com or thenews.com has to know my google account.
That kind of depends on what sort of service.
kind of a indiehackers.com product hunt but idea based. something to keep track of all my project ideas
for me it might be twitter because it's almost like a throw away login for me.