Always best to stay with the manufacturers paper - they test the inks on their own, so everything is calibrated around own-brand; printer, paper & inks.
The type of paper will depend on the type of image, I print mostly in HP Premium Plus Glossy, but if you had close-ups of animals you would be better with a slightly textured paper, as this will highlight the fur/skin etc. Most manufacturers supply a sample pack of different papers - try getting one of them & playing around with them?