Conspirator chains are easiest to set up in a deck of non-terminals. But without some kind of way of drawing more cards into your hand (for instance, if your non-terminal is Laboratory), they are frustratingly difficult to put together in decks and quite prone to bad draws–especially as you clog your deck with Victory cards. So Great Hall/Conspirator, for instance, can only work in extremely dense concentrations (which, in the absence of strong trashing, will take too long to set up).
Warehouse, however, is a good way to get Conspirator chains working at significantly lower density by filtering out non-essential cards. It speeds up the process tremendously and allows Conspirator-based decks to compete tempo-wise with other strategies. Of course, it works best in combination with other cards that do well with Conspirator (Laboratory, Grand Market), but Warehouse and Conspirator are usually good enough together on their own to form a viable deck in most sets.
As usual, this combo works far better with Warehouse than Cellar; you’ll rarely be Cellaring more than 3 cards, and the ability to view your drawn cards a priori makes a huge difference.
A pretty straightforward game, where both of us go for the combo. Our strategies are helped out a bit by Worker’s Village and Laboratory, two great helper cards for Conspirator decks.