Any build can have taming. It all depends on what else you want to do besides taming.
generally speaking a full tamer with highest level pets wont be able to ride a horse so foot speed is important. This means Alvarians. Also healing your pet will be very important. Mages do this the best.
Alvarians are great at archer/tamer, or mage/tamer. The playstyle will be fast, mobile but fragile. A lot of kiting involved.
otherwise, the other races will complement a warrior/tamer. Each race in their own particular way. Human will give you most flexibility, Oghmir will give you tankiness( but slow). Thursars best melee damage/combat regeneration.