Chopping is good, because it gives you a quick gift of a large amounts of production. But don't become dependant upon it, or your game will be crippled. After all the forests are gone, you get production from resources; terrain like hills and plains; and improvements like watermills, workshops, and most of all, mines.
Chopping is great, but if you become addicted it will negatively affect your gameplay.
As for Windmills v. Mines, it depends upon the situation. Do you have enough food to support the mine? How much production does the city already have? Is the city going to be one of your major production centers, or is it going to be a commerce or GP city, or a mix? It really depends upon the situation; there is no absolute best answer. Generally the AI builds many windmills, I build more mines myself. But I am very focused on production as opposed to commerce, at least in the early and mid game.