You can check out the book on how to buy with low money down by Mr Turner on BP for more creative ways.

Multiple low ball offers...

My usual approach is to find 3/1 or 3/2 single family houses in a good school district, but my budget will be rather low for this move since my family is staying in OH and we'll be running two households. 

What is the most important quality?

Interest only, low interest cost, can be tax write off.

My offer on a REO was rejected as too low - the issue with the townhouse is listed at (1)"system did not hold pressure due to damages, unable to find source of allleaks, water heater damaged at side where TPR valve damaged" and (2) "Water Supply and Sewage system was inspected for presence of obvious visible defects.

Being licensed I will get paid a commission on the buy or the sell or both in some cases and he will get paid by buying low and selling high on the homes that I find him.  

I would replace with batt insulation if you are doing it yourself...easier to work with and readily available from Home Depot, Lowes, etc.  

I can bring construction knowledge and a team of competent contractors who will provide quality and most importantly cost efficient rehab work.

You will likely have a difficult time finding an agent to prepare a low ball offer like that because the likelihood of winning is so low.