How do I choose the calcium supplement that is right for me?

Read labels. Use calcium citrate, it's better absorbed than calcium carbonate. Shoot for around 1000-1200mg a day combined in food and supplements. If you take a supplement don't take any more than about 600mg at a time because you won't absorb more than that all at once. And don't forget about vitamin d3. You can find a supplement with both calcium and D3 in a combined pill. And generics are fine.
Dairy products. Milk and yogurt provide an excellent source of calcium and phosphorus (also necessary for bone health). 8 ounces of either provide about 300 mg of calcium. Three servings a day provides adequate calcium. Calcium carbonate, calcium citrate and calcium phosphate are good supplements. One might be better tolerated than the others.
Trial and error. Generally all calcium supplements are well tolerated but some individuals may have minor side effects with one or another. Constipation is probably most common. Calcium carbonate is fine to start with but others can be tried if it is not tolerated.