I made a Breton, so does the familiar level with me?

While we're on the topic-- how does the Familiar compare to zombies and atronachs in the conjuration tree?

Sort of. The cost of the spell actually goes down as you level your Conjuration skill (even though the strength and duration remain the same). I posted the link on UESP here:

http://www.uesp.net/wiki/Skyrim:Magic_Overview#Spell_Cost

Also, dual casting perk increases the power of the conjured familiar (or any summoned creature for that matter).

The Familiar is the lowest level conjured beast. As you level the skill, you can cast better summoned creatures (Flame Atronachs, Thralls, etc.)