I suggest a Wizard with a focus on the conjugation school of magic. Certain classes also have subclasses that focus on a familiar/pet. The Warlock pact of the chain gives you an incredible useful familiar in the form of an Imp, a Quasit, a Pixie or a Pseudodragon and they are plenty of eldritch invocations that buff your summon and make them more useful both in and out of combat.
