Hi Texas girl.
Considering Strawberries are quite happy in grow bags...I think anything around six inches or so is fine for them.
You will however have to remember to water regularly if you do have shallow soil as it will have no resevoir for the plants to tap into. Also a regular feeding to keep the nutrient level up.
As to planting..if the soil is fresh then just plant with a little slow release fert.
It might be a good idea if you did a check on the soil to find its Ph.
Straws do not like acid soils very much.
An apple a day.....keeps me in work.