What earth organisms would survive if they arrived on Mars? Contaminating other planets is a concern in space exploration. My question is what organisms, or small collections of organisms, from earth would be able form a self-sustaining population on Mars? I'm not worried about how they might get there, so deep sea microbes and the like which would have to be purposely transported are in scope.

This is not the same as this earlier question, as that one does not consider sustainability.
On the surface of Mars probably none, since it's too dry or too cold, or both, to stay active.

Spores or other dormant forms probably could survive for centuries, until radiation will gradually destroy the organic molecules necessary to get back into an active state.

But there are "Mars Special Regions", where either Earth microbes or potential Martian microbes - if some exist - cannot be ruled out to be able to spread.

Things might look quite different in the underground, especially in warm and wet zones, which may exist by geothermal heat and ground water.
There, at least lithotrophic bacteria/"chemolithoautotrophs" could survive and spread.
Those could then form a basis for a food chain of other organisms.

Plants dependent on sunlight, or animals dependent on oxygen would hardly survive.

For a list of species, see table 2 on page 895 of the above reference paper. The following species and genera are mentioned in the table:
Psychromonas ingrahamii, Planococcus halocryophilus strain Or1, Paenisporoarcina sp. and Chryseobacterium, Rhodotorula glutinis (yeast), Colwellia psychroerythraea, Nitrosomonas cryotolerans, (lichen) Pleopsidium chlorophanum.