My printer is an Epson 3800 with K3 inks. I tested about 80 different papers and have reached a strong opinion about what my favorite papers are. Please keep in mind different printers and different ICC profiles will give you different results, so take my suggestions with that in mind. I also hate warm paper (looks aged from years of attic storage; besides I can tint myself), so my picks reflect this bias.
Favorites:
1. For best results (and the most expensive), I use Epson Exhibition Fiber paper combined with a high gloss varnish spray. The varnish gives it that "lip gloss" look that I love. Baryta papers are hard to spray because their surface is so smooth. EEF has a lovely subtle texture that barytas lack. I get better results with my custom ICC profile using the ColorMunki than I do with the Pixel Genius profile.
2. For second best results (and best value), I use Ilford Smooth Pearl. I don't varnish this paper. I was shocked how accurate the manufacturer's icc profile worked with Ilford papers.
3. For practice printing I use the Ilford Luster Duo. You can print on both sides. Saves money.
4. I don't print with matt black ink, but my favorite MK paper is Epson Hot Press Bright.
The baryta papers look good too (e.g., Harman Gloss Baryta and Ilford Gold Fiber Silk) but they have no texture. No texture looks cheap to me (don't know why). Plus they scratch like the dickens. But technically baryta papers will give you perhaps the best image quality (color gamut, dynamic range, etc).
My favorite metallic paper is from RedRiver, which came as a surprise really because I didn't care for their other papers compared to my top choices that is.