First and foremost, the original artist must do all their own developing and printing of their work, this is what distinguishes a photographer from an artist. An artist knows everything about their entire medium while the photographer does not. One of the most important aspects of a fine art photograph is in knowing that the expression is being presented the way the artist desires it to be, and this can only be done by the original artist, not a photo lab technician in timbuctu. Ask any photographer who has their work printed for them if they have always been satisfied with the final photograph and you are likely to hear that they are not. It isn't worth the paper it's printed on if some photo lab from timbuctu does the printing - this is simply a distinsion between fine art and what one might call commercial art.
Second, the paper and processing quality must be the absolute best available. for color photographic art the Fuji Crystal Archive type CDR paper is currently the best for color photography from a longevity and color saturation standpoint (see www.wilhelm-research.com - an independent research company that determines the life expectancy for different photographic print materials - in fact Cibachrome, now called Ilfochrome classic deluxe, at one time (some 20 years ago) was considered the best material available, sadly it now ranks as one of the least archival materials available - oh how times change); while selenium toned photographs from a paper with a high silver content should be expected and demanded for all black and white photographic art.
Finally, it should last! many museums and corporate collectors are now seriously investing in photographic art as an investment. why? the primary reason is the archival quality now available. in fact the process and paper that i employ has an archival quality estimated somewhere between 250-500 years (depending on how you care for it.) time frames like this outlast many "traditional" mediums. insist on archival quality and only the best photographic materials and museum standards.