Hybrid, touring, or road bike for new commuter? I live in Los Angeles and have a 2hr commute to UC Irvine by train with bus connections on either side. After doing this for a year, I am looking to start bike commuting to and from the train stations to get back in shape. Because the routes are so different, I'm wondering which bike type is best? 

The ride to school is 2 miles with a downhill incline to Union Station on a busy street without bike lanes. Then I can hop on the train with plenty of bike racks. The ride to school is a nice 6 mile ride in paved bike lanes and paths the entire way, and very flat. I would ride the opposite way home, but the ride is slightly uphill the entire 2 miles home in busy traffic. 

A road bike sounds like a great option for the 6miles near school, but would this hold up well on a busy paved street in Los Angeles? I'm just starting to get back on the bike after 15+ years with I borrowed mountain bike, so I know I can make the trip at least :)
8 miles each way is a reasonable commute.  

In the city a pure road bike is not as stable.  

You should test both flat and drop bars to see which is more comfortable for you.  Drop are a little more efficient but that is not a long commute.  For an uphill I think flat bars are fine.  

A full touring bike is probably more than you need unless you are looking to mount racks and also using it for longer rides.  And you probably don't want rack or fenders loading it on and off bus and trains. 

Look for mid sized tires (like 32mm).  

A light bike is also nice for getting it on an off bus racks.

The also have styles of bikes called urban or city.    

Even a mountain bike with street tires would work.  Not a first choice but if you found a good deal used.  

A local bike store (LBS) will help you out with fit and selection. You can get some decent new bikes for $600.

If you are on a budget then CL but be careful.    

I like a cyclocross bike fit with touring tires for commuting but maybe not the optimal for you.