Which houses have an Alchethe table WITH an Alchethe Satchel

Every home except for the house in Whiterun has an Enchanting Table upgrade availiable, as well as the option to procure Alchemical facilities.

If you want a home with a Smithy, you must have the Hearthfire DLC installed. This allows you to buy land and build a house in 3 holds: Falkreath, Morthal, and Danwstar. There you can build your own smithy. Other than that, there are no houses with forges in vanilla Skyrim. Riften and Whiterun offer the most convenient access to forge facilities, though Riften's forge lacks Smelting equipment.

The only containers in the basement of Proudspire manor are the barrels in the back room with the cot and the barrel next to the weapon rack.

I believe this is a house mostly for displaying stuff with multiple weapon plaques, mannequins, and weapon racks, and lots of book shelves. Functionality wise its not the best.

However, its the only house with a safe as a container in the main bedroom.