I agree with QuiltE, felt didn't work for me. I used black batting, but the fleece would be less expensive. My board is made of foam insulation. My DH nailed a strip of molding along the wall, and my board rests on it with Command strips holding it to the wall, which means no big screw holes in the wallboard.
For all my little bits n bobs, I bought an office-supply drawer insert with various sizes of cubbies. Rather than staplers, rulers, and erasers, mine holds boxes of pins, thimbles, seam rippers, marking pens, etc. You could probably empty your bucket into one and actually find things.
I think my only real suggestion si, don't do anything permanent until you have lived in and sewed in there for a while. I ended up rearranging a picture-perfect space because it didn't function the way I had hoped. Enjoy your new space!!