Should be decent, lightweight, async, up to date, with the support of http/2. Or any of these combinations.
What do you recommend?
I moved this thread to Using Swift as it does not pertain to Swift Evolution. 
Well, I just pushed a new release of Siesta, which in my biased opinion is worth a look.
It’s a structure for client-side state management — preventing redundant requests, sharing data across sections of the app, keeping things in sync, preventing race conditions & consistency issues, etc. — and not just an HTTP client per se. If instead you are looking instead for just HTTP with no additional structure, Foundation’s URLSession is the API to use. It is all the things you listed. Alamofire is very popular as well. IMO it doesn’t add much for most users, but can be very helpful for certain things such as SSL customization that are difficult to configure in URLSession.
lightweight, async?