For a smooth matte/matt/mat paper I prefer Canson Rag Photographique 310 over the more popular Hahnemühle Photo Rag 308. The Canson paper stays flat, the Hahnemühle paper has a tendency to curl after printing. For landscapes, the Hahnemühle can muddy dark greens. The Canson paper also has no OBAs.
I like BFK Rives for a very lightly textured paper. In the fine art world it is known as Rives BFK and is a traditional fine art printing paper.
For a medium textured paper, I really like Hahnemühle German Etching. It retains a lot of detail for a textured paper. I’m currently looking for an alternative in 100% cotton, which I find sells better, and without OBAs. If it was only for my own use, I would not be looking elsewhere.
For a heavily textured paper, I like Arches Aquarelle. But once you get into heavily textured papers, you get even more into personal preferences and suitability for individual images. There are lots of good watercolor papers about.
I also use Breathing Color Elegance Velvet and Pura Velvet.
One thing worth mentioning with regards textured papers is the loss of texture where the ink goes down. On some papers you can lose almost all texture in ink saturated areas, and only retain texture in the whites and lightest colors. Other papers will retain texture uneven under heavy inking, and some will lose texture even with little ink. It is worth testing textured fine art papers under different ink loads and with a variety of test images. A heavily textured light skinned face, for example, generally doesn’t work well unless the image is very large – probably larger than A3+.