From the fairly extensive research I had done before selecting the supplements I would take, I found that calcium citrate is generally regarded as the most easily absorbed and bioavailable form of calcium. Here is one comparison between the citrate and carbonate forms:
and here is a general info page about calcium:
I personally use the following:
Now Foods, Calcium Citrate tabs (with Magnesium, Zinc, Copper & Manganese)
Be aware that these are fairly large tablets (but well-shaped, so at least for me, easy to swallow), so if you need capsule form, they're also available, but more expensive per unit of calcium ($0.23 per 600 mg Ca, vs. $0.10 per 600 mg Ca for the tablets):
Be sure to take magnesium with your calcium, for proper Ca absorption. The optimal ratio of Ca:Mg to take varies, depending on which source you refer to; it can range from 1:1 to 3:1; I aim for 2:1 (which is the ratio in the tablets above).
Beware of calcium in the form of MCHA (microcrystallinehydroxyapatite); this form is usually derived from animal bones, which can contain heavy metal contaminants. I try to avoid MCHA altogether, to be safe.