So I bought an expensive manor in Solitude and I check out the basemant which has my enchanting and alchemy tables but one very important thing missing. Containers. I spent 25K gold on this house and I don't even have containers near my tables? I'm a forgetful person so everytime I forget one thing I have to run up and back downstairs just to get one item? And is there some way to move around containers in my house because that would by awesome, if not, the house in Solitude is just a waste of money when my 5K Whiterun house has a container near my alchemy table.

Nope. You could use console(pc only) and add some more stuff. But other than that, the house decorations are static.

The best you could do would be to put things In a basket. If they even stayed in it.