Thanks for taking the pictures. Those pictures are like going to an art gallery and taking a picture of Mona Lisa's nose. LOL. Reminds me of some of the pictures I took when I started this job. Any chance of getting some non-close ups?
How to define the problem. Hmmm. The better defined, the clearer the solution, right? Can you go deeper than "stuffy in the basement"? Is that the whole and only problem?
You certainly don't want to cure one problem then "oh yeah, I forgot - we have this problem too". Sometimes multiple problems indicate a whole different course of action.
Really the house is a system of systems. If you focus the way you took those pictures, you may find yourself going around in circles throwing money at problems.
You don't list your location in your header, so the advice you get will not be location specific. It's best to step back and get an understanding of the whole house, then drill in on problems. (Ie: sometimes an issue in the basement is caused by a problem in the attic, but if you never leave the basement you'll never figure that out.)
Some places you can find knowledgeable energy auditors, in other you can find energy raters that can help.