An unglazed ceramic vessel should help to regulate the moisture issues that many of the others have mentioned (which would be true in a glass jar).
Glass jars are also problematic as they act as small greenhouses, with the light warming the jar which can cause it to spoil faster.
I would recommend that you fit what garlic you can into the container as whole bulbs/heads, then add your remaining garlic broken up into smaller bits (unpeeled cloves or clumps of cloves). As you use the garlic, use the fragments first, then break into the whole bulbs.
But the more important thing is to only buy as much garlic as you're going to use in a reasonable amount of time. If you're not using up your garlic within a month or so, you should probably be buying less garlic each time.
The whole/fragmented method should allow you to tell your older garlic from more a more recent shopping trip -- empty the jar, put the new garlic in as whole bulbs, then break the older garlic apart and fill the jar.