I've used Super Shuttle from that airport and it got me into town without too much extra time (occasionally it feels like you are in those shared vans for hours if there are multiple stops).  One thing that's nice about their shuttle service is if you have a frequent flyer rewards you can earn extra miles by using Super Shuttle.  All of those miles add up so for me that's a win! Here's a link to see more about how that works. 

http://www.supershuttle.com/blog/Blog/tabid/947/Article/106/earn-frequent-flyer-rewards-the-next-time-you-need-a-lift.aspx

I always use UberX from San Francisco International Airport. It's reliable and you can see that the driver is actually on the way, and it's often cheaper than a taxi. You can also typically find a free coupon code online for your first ride. Try Lyft as well. 

I just checked my Embark iBART app (which you should download for the trip to get BART schedules!) and yes, getting in at 11:50 PM is too late to ride BART as the last train out of San Francisco International Airport to the Union Square area is at 11:54 PM.  

You could look into a shuttle, but I'd personally prefer to get a Lyft, Uber, or Sidecar, especially since there are two of you.  It ends up being about the same price as taking a shuttle, minus all the stops.  If one of you has a smartphone, I'd download all three of those apps as they all have different availability and pricing.  They'll be really useful for getting around San Francisco as well.

Let me know if you have any other questions and I hope you have a nice vacation! :)

Booking a shuttle in advance is probably the cheapest and easiest solution. Uber is a possibility or taxi. The trains definitely aren't running after midnight.