How to choose a sub driver?

Many years ago with the help of people in this forum I built a sub with a driver I had, a 10" which was pretty good.

That sub has been dismantled years ago. And I'd like to build a new one, to go low.

The room I'm running it in is only 3x6 meters so it doesn't need to be ridiculously loud. But I'm trying to find a good driver. The problem is that there are so many of them out there in the market, and I have no idea where to start

How can one tell if a driver is a good candidate? What specs should i look? Is it possible to look at the T/S parameters to quickly discard bad candidates?
 
The main speakers are Yamaha NS-50F which claim to go as low as 35Hz. But there is a LOT of excursion and not much substance in very low frequencies (LFE channel). It's more than appropriate for music at moderate volumes, but not for LFE in movies.