How do I know whether I should use dolomitic or calcitic lime?

Dolomitic lime is generally higher in magnesium than calcitic. Ultimately, it's dependant on looking at complete soil test results that include calcium, magnesium, and sulfur levels, along with crop requirements.

“If a soil is low in magnesium, dolomitic lime should be used; otherwise, calcitic lime can be used. Many organic soils and some piedmont soils are naturally high in magnesium; most sandy soils in the coastal plain have little magnesium. The soil-test report will indicate which lime should be used. A magnesium fertilizer could be used instead of dolomitic lime, but the cost of this treatment is almost always considerably higher. Dolomitic limes are slightly more efficient in neutralizing soil acidity and may have CCE values greater than 100, depending on purity.”