So the cheapest Castle is $3, but why stop there?
Ruined Castle
$0
Victory - Castle - Ruins
Worth 0 VP
Overgrown Castle
$1
Victory - Castle - Shelter
Worth 0 VP
When you trash this, gain a Castle.
Fool's Castle
$2
Victory - Castle
Worth 4 VP if you have any other Castles, otherwise worth 0 VP.
Alchemist's Castle
P
Action - Victory - Castle
+2 Actions
While this is in play, your other Castles are also Action cards that give +3 Cards when played.