What is the best keyboard to connect to your phone?

You need to be way more specific about use cases and your phone platform.

That said, I see a lot of people using Logitech K380s with their phones. Well, I don't see a lot of people using keyboards with their phones, but when I do, it seems like a K380. I do own a K380 myself, for phone and iPad use. It is a nice, compact, durable keyboard but I rarely use it.

I've connected my apple magic keyboard to my phone before, mostly just to see if it worked. It's a small compact thin and light keyboard. I'd imagine most keyboards with bluetooth these days probably connect, just depends on what kind of form factor you're looking for