I am trying the famous Ilford Gold Fibre Silk (US link - UK link) paper for printing. Just made one print so far, the photo is the top one here, and it's promising. It has the depth-enhancing qualities of glossy paper, but it's a "silk" surface, so you don't get as much irritating reflections in the surface. It's a very pleasant surface too.
And interesting characteristic: you'll notice that the photo has some very dark areas, which I did not lift because I like the twilight atmosphere they give the photo, the impression of the sky is enhanced. And in my experience until now, prints have always had less detail in the shadows than seen on the screen (perhaps because the screen is back-lit). But apparently with this paper, the print has more shadow detail than is seen on the screen! Very strange, and it may be an advantage, we'll see with more experience.
Update: I made a comparison print on the Hahnemule matte paper, and it's equally nice. No easy choices in this world.