This review from 2007 is the only comprehensive assessment of the various types of calcium salt forms. Suggesting that calcium citrate can be taken without food and is the supplement of choice for individuals with achlorhydria or who are taking histamine-2 blockers or protein-pump inhibitors.
Straub DA. Calcium supplementation in clinical practice: a review of forms, doses, and indications. Nutr Clin Pract. 2007 Jun;22(3):286-96. doi: 10.1177/0115426507022003286. PMID: 17507729.