I only consider unrated challenges with minimum of 3 days/move. In unrated games I don't usually use separate analysis board, books or databases but if someone wants to use them against me that's fine.
In my rated games I use all permitted resources. I have long experience playing otb and have found correspondence chess good way to improve the general chess knowledge. I often move slow and altough this may occasionally mean that I'm actually doing some analysis more often I'm just planning to study the position deeply next day before realising I'm deceiving myself.