Gary A Sounds like a great project. This was a very popular type of construction, and there are a few specialty companies who specialize in that type of work today. Take a look at my article A Building and Remodeling Checklist . I think that you will find the information useful. In this case you will have to get some expert help regarding the structure and the temporary support.
Basement is concrete block.
Would like to just glue 1x3s against the block and frame the outer walls with 2x4s. The door would be in the 6 foot end giving me two 10' long spaces. I plan to use one rod on the left side for full length garments and two rods on the right for shirts, etc. If you don't recommend glueing 1x3s, should I use 2x4s on the block walls fastened lengthwise or make a plate like I have to for the outer walls. I would not glue any material to the block walls.