Epson actually offer decent papers in most of the main categories of inkjet papers suitable for pigment ink inkjet printers. I summarise some of the most important / commonly used ones below:
Enhanced (or Archival) Matte: Decent matte paper, suitable for learning your way through matte fine-art type printing. Good for proofing for more expensive papers e.g. UltraSmooth Fine Art). Smooth surface. Decent but not the best of max density or gamut. Base colour quite neutral white. A bit on he light/thin side compared to 'proper' fine art matte papers. Might warp a bit if too much ink is applied. Contains lots of UV brighteners, the base will get more creamy / yellowy with time.
UltraSmooth Fine Art Paper: The fine art version of the Enhanced Matte, so to speak. Surface similar to Enhanced. Thicker / heavier. Warmer base due to absence of UV brighteners, 100% rag base. More archival qualities than Enhanced. Excellent paper up there with the best.
Velvet Fine Art. Medium textured fine art paper. Warmer base. Archival quality. Very good dmax for a matte paper. Excellent paper. 100% rag, some UV brighteners. Excellent paper up there with the best.
Watercolour Radiant White: Good value watecolour like surface (textured). Adequate weight. Off-white base. Not 100% rag, but very good archival qualities. Not too good details.
Premium Luster: Probably the best of the Epson glossy type papers. Nice 'luster' type of semigloss surface. Excellent in the category.
Premium Semigloss: Pearl type of surface. Not too bad, but I would prefer Premium Luster.
Premium Glossy: Smooth semigloss type of surface. I prefer Ilford Smooth Gloss for this application.
Epson currently do not offer papers in the following two categories (to my knowledge):
1. Hi Gloss type of surface (e.g. Pictorico reminiscent of Ciba/Ilfo Chrome)
2. New category of pearl surface (with some shine and light texture) rag papers reminiscent of traditional BW photographic papers (e.g. Hahnenmuehle Fine Art Pearl, Innova, Crane Museo etc).
For the rest of the categories, most of the decent third-party papers you can buy will broadly fall in the categories of the Epson papers I have listed above, give or take some texture, base whiteness, weight, archival characteristics, dmax and gamut.
Hope the above helps.