There are two lineages of basal carnivores, probably most likely most similar to martens or civets.
One of the populations that descended from the one bloodline, the Feliforms, eventually gave rise to the cats, hypercarnivors specialised for the hunt. Another specialised lineage among the descendants of this branch are the bone-breaking hyenas. There are also several more conservative taxa called “civets” - the most basal lineage being the African palm civet, the linsangs being the sister taxon of the cats, the vivirids, the mongooses and the radiated carnivores of Madagascar, the latter two forming the sister clade of the hyenas.
Meanwhile, one of the lineages that derive from the other branch, the Carniforms are the canids, who are the most basal extant branch. They eventually specialised in running. The next most basal are the bears, who would eventually become massive creatures. Another group would be semi-aquatic animals that would over the course of the ages evolve to be ever more aquatic, eventually becoming the most specialised group of the carnivores, the seals. Their sister group are the mustelloids containing the raccoon and allies, the mustellids including weasels, martens, badgers and the wulverine, the skunks and finally the Red Panda.
Extinct families are the Nimravids, the most basal specialised branch of the Feliforms that convergently evolved the habitus of the sabre-toothed cats before true cats evolved; the barbourofelids, another group of false sabre-toothed cats, where it is unclear if they belong with the nimravids or are the sister to the true cats; the Percrocutids, who had a habitus and ecological role similar to that which their sister group would evolve later; and the bear-dogs, basal Carniforms who had traits reminiscent of both bears and dogs.