Is there any particular bacterial lineages which contain a large number of endosymbiotic species and that inhabit a large range of eukaryotic hosts? To me, this would seem to suggest that they are particularly well adapted to becoming endosymbionts.
Members of the genus Xenorhabdus are entomopathogenic bacteria that associate with nematodes. The nematode-bacteria pair infects and kills insects, with both partners contributing to insect pathogenesis and the bacteria providing nutrition to the nematode from available insect-derived nutrients. The nematode provides the bacteria with protection from predators, access to nutrients, and a mechanism of dispersal. Members of the bacterial genus Photorhabdus also associate with nematodes to kill insects, and both genera of bacteria provide similar services to their different nematode hosts through unique physiological and metabolic mechanisms.