"Human" seems like the word. It seems that most people feel that "Human Rights" = "My Rights".

"People", to me at least, seems to carry the connotation of homo sapiens whereas "human" seems to refer to that quintessential, luminiferous, undefinable essence that takes a set of organisms and makes us want to give them human rights(i.e., my rights). For other people, the roles of the words may be reversed. But then they may want to refer to "People Rights" rather than "Human Rights".

For example, I'm fairly conservative and grant human status to vertebrates and cephalopods. Some people are more liberal and restrict their definition to only, say, great apes, cetaceans and mammoths. Some people are even more extremely liberal and only grant human status to certain members of one particular species of great ape.