What is the difference in using just a crystal on the pic or using it with
the 2 capacitors?
As usual, a quick look at the 200 page data sheets for the 16F876 didn't
produce an obvious answer so I assume someone here knows.

I have been running with just a bare 4MHz crystal on osc1/osc2 and no
capacitors, and someone told me that's fine and capacitors would probably
cause trouble if anything for me since they have to be properly calculated
etc.  He said he is putting capacitors on his circuits though because his
will be going outside and he wanted some stability.

So how does one decide?

Also what's the difference between crystal types?  I am using "general
purpose microcontroller" parts but there's those other series or parallel or
other specific types.  Again how would I know what to choose?