What features should I look for in a vessel for making Indian curd (yogurt / Dahi)?
The slight ability of clay to soak up whey doesn't matter, you won't really notice much difference with it. Just use any vessel that is convenient - glass, metal, plastic, glazed or unglazed clay, other ceramics will all work. 

If you want curd without whey, you have to use a method which produces less whey (usually, that needs slower fermentation at lower temperatures) and/or strain the curd. Do it in a cheesecloth overnight under its own weight, don't press it like paneer. The vessel is not important. 

In principle, better isolation can give you more stable temperatures and thus ensure better fermantation, possibly giving you curd with less whey. In this sense, the thicker the walls and the less heat-conductive your vessel, the better for curd. This would be a reason to use clay, ceramics or glass. But it can be easily offset by using more isolation for your fermenting environment.