Welcome to the board Kendra! My basset was actually very good & a fast learner, but I hear that some bassets can be especially challenging to potty train. It's important to note that in general bassets are *not like* other dogs in many ways. Potty training & the whole "obedience" thing especially.
After any activity (eating, sleeping, playing, drinking) I would take José outside and when he would go, I would be so crazy happy and praise him. He caught on pretty quick but with bassets you can't slack... you need to go out A LOT so they can't slip up.
I trained him to go on paper the same way, outside I would put a piece of newspaper down and let him go on it and also get all excited. If I ever had to leave him for a bit I confined him in the tiled puppy-proof kitchen & put newspaper by the door we would leave from. I never really liked crates. I confined him to a room, with a bed on one side & potty papers on another, plus some toys.
I'm a little worried about your love of a "clean fresh smelling house" because bassets might have been put on this planet to obliterate that... Good luck with the shedding and drooling!