Like most of us, I have a few different types. Two that haven't been mentioned so far are the Safari or Boonie sling, which is great still hunting or in some country where having both hands free, but the rifle easily accessable, with minmal movement, is a big help. No use as a shooting aid or in alpine areas.
The other is the Magpul RLS. 1.25" and works fine as a carry strap AND as a shooting aid. Once the loop is adjusted (before going afield) it is very quick to sling up without cinching up the loop. Carry strap length is adjusted independently from, and without affecting the loop size. They come with plenty of length and I haven't been able to bring myself to chop the surplus off my two. Bit like shortening a barrel - easy to do - hard to undo.
For no particular reason I don't like Cobra types. Also have a simple Murray which is very traditional and nice, but of limited use as a shooting aid.
The problem that I have with a quick wrap in a carry strap is that the correct length for the wrap is seldom the same as the preferred length for carrying. The RLS solves this.
As for swivels, Recknagel trumps the quality stakes, but may not have a wide enough loop option to suit some tastes. I think the swivels that I bought from Trader Keith a few years ago are Recknagels.