So, I've just become a Vampire Lord and I can't help but feel like the character I'm playing is going to make a really weak VL. Does your base magicka have an effect on the VL magicka? or is it kept separate?

Nope. My warrior who hasn't put a single level up into magicka can fling loads of spells in VL form. The bigger spells are quite a drain, but you can always mist form to recuperate, and your claws are plenty effective too.

I have read that a mage with conjuration specialization makes the best use of the VL abilities.

I assume you have no rings or other apparel in VL form?