Some makers have swatchbooks, others have sample packs. AFAIK Hahnemuhle have sample packs only. Permajet have a swatchbook. Harman have sample packs, etc.
At big shows you can find many sample packs, often printed with the names of the media on the back.
HP media are indeed spec'd for their requirements. In most cases they are built upon the paper mill's already good base, but exceed the qualities of generic coatings to a degree that has to be seen to be believed. The permanence however is not going to be improved in way of the base, but perhaps slightly in the way of lightfastness.
If anything HP printers are running better on their own papers, whereas Epson can print on quite a few more surfaces without problem. The quality with HP printers and HP papers though can rival any other system and combination with certain image types.