What kind of herbs are common in Italian dishes? Yesterday I tried to follow a pasta recipe that called for tarragon.  Since I didn't have this herb, I sustituted basil.

For convenience, I may try to plant those commonly needed herbs myself so I can pick them fresh, when I need them.

What are the most common herbs used in Italian pasta dishes and should they be used fresh?

Please state why the herb was chosen rather than simply listing them which would not be that helpful to me.  For example, tarragon goes well with chicken so I put some into the pasta dish because I like the fennel-like taste of it.
Some example of herbs usage here in Italy (I'm 100% italian living near Milan):

Basil: (for its fresh taste)


Pasta with tomato sauce and a couple of leaves of fresh basil on top.
Pizza Margherita: Mozzarella Cheese, tomatoes, basil. 
Pesto: basil, parmigiano cheese, pine nuts &amp; olive oil.


Oregano: (a little salty, chosen for its strong parfume)


On top of Focaccia
Mozzarella Caprese (mozzarella, tomatoes, basil &amp; oregano)


Sage (delicate perfume, used to enhance flavours)


Gnocchi with butter &amp; sage, with little parmigiano


Parsley


Mostly used with fish pasta dishes (never with meat!)


Some common mistakes on italian pasta recipes "as seen from abroad" is that we don't really use parsley or oregano everywhere. Many other herbs like tarragon, marjoram, etc... Are rarely used in everyday recipes.