Whatever you get, price in a setup with a reputable setup/repair guy. It will make all the difference in the world.
+1 on getting a good set up on whatever you chose - can 100% be the difference between a budget friendly bass being awesome or discouraging.
I often think a great first bass is a P or J based design. Simply because it introduces the player to the two most common styles of bass (in particular P or JJ pickup set-up) and allows them familiarity with the industry standard sound. I also think there is no need to be distracted by active pre-amps and what not when learning the basic fundamentals of the instrument. Once they have the basics down - well heck the world's you oyster.... so I would also suggest a VM Squier as its under your price point or a used CV Squier.....or SX P or J but as said above a good setup by someone who really knows what they are doing will make all the difference