Wallabie’s answer is excellent. I’m not sure where you are getting your soil tested, but if it is at a State University Extension office, the agriculture agent there can tell you which tests are essential for your area. I’ve been a Master Gardener for about 20 years, and generally just get basic tests for nitrogen, phosphorus, potassium and pH done. Wallabie’s advice about soluble salts is right on target.
Although nutrients are important, you really need to get your pH tested. Most plants like a fairly neutral soil pH—somewhere around 6 or 7. Berries, potatoes and a few others like lower pH. Here’s one of many online articles about pH:
http://hubcap.clemson.edu/~blpprt/bobweb/BOBWEB29.HTM
University Extension Service Agents and Master Gardeners are required to provide information on both organic and traditional gardening methods. Generally their services are free or very low-cost, so I would encourage you to contact them either in person or via e-mail.
Finally, as an organic gardener you will find that compost is your best friend. The tilth of your soil is just as important as your nutrients and pH.
Best wishes for a fantastic gardening season!