Great minds think alike!
I did something similar last night. Although I used mostly dried mushrooms. Mine was:
Dried porcini mushrooms
Dried morel mushrooms
Dried white mushrooms
Small dice fresh white mushrooms
Butter
Olive oil
Garlic
Scallion
Sage (could have been almost any other herb, though)
Heavy cream
S & P
I soaked the dried mushrooms in boiling water to rehydrate them, then chopped them and strained the soaking water. Sauteed all the mushrooms in butter and oil, added chopped garlic, thinly sliced scallions, and crumbled dried sage, cooked some more, finally added the soaking water and a splash of cream and boiled it down.
That's a pretty basic sauce that could have gone over anything (I used it over mushroom-and-cheese filled tortellini).
Obviously, with all fresh mushrooms, there wouldn't have been any soaking liquid, so then I'd have used red or white wine -- but added it earlier so that it cooked down a lot -- and stock. Which kind of stock would depend on what I was serving it with (although made with vegetable stock it could go over anything). And I added cream in this case only because I had some; normally I don't, and so my sauce would be creamless. Not as rich, but still good.
But enough about me.
You are on the right track with all the ingredients on your list. This is one of those sauces that can be played with a lot. Also try shallots, if you have them, instead of onion and/or garlic. Thyme is another complementary herb, too. Just follow the basic procedure of sauteeing the mushrooms (and aromatic vegetables), then adding your liquid(s) and cooking the whole thing down to the consistency you want. Could hardly be easier!
And while you asked about using your new saucepan, in addition to making this kind of sauce on its own, you can do it as a pan sauce: that is, after you've sauteed or roasted your meat or poultry, add the mushrooms to the cooking pan, cook them and whatever aromatics (onion, garlic) you want, then add your liquid and scrape all the "fond" (the browned juices) into it to dissolve.
Mushroom Sauce 
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