Pines will rot the fastest, and turn your soil (Acidic), Hard woods will last longer and will end up harvesting bacteria. You will not be able to preserve the initial look of the tank when it is setup... Take a photo to remember it, and let nature take its toll. Molds, mosses, and fungus will add a natural look to your tank. After the initial "Outbreak", or, "Infestation", your wood will normalize. The nasty fuzzy mold, and slimy fungus will die down to tiny spots, and hopefully the moss will prevail and make the rotten log appear as if it were part of the terrarium. If you are lucky, you may even get some plate mushrooms growing on the log.
I rain my tank every week, and fog bi-daily. Just make sure there are two screened holes at opposite sides of the tank, so that there is some circulation to limit bacteria and promote drying. You don't need heat to dry a tank, only a steady flow of arid room temp air (Humidity 50%). Always drain the excess water in a tank.
To drain my water, I lay a lizard mat in the bottom of my tank before dressing it up with substrate and stone. In one corner, I have a clear tube that goes down to the lizard mat. I siphon out the excess water about two hours after it rains, then again, two hours later. (The second time is to allow the rest of the dripping water to drain.) I use a standard fish hand siphon pump that is used for cleaning the bottoms of fish tanks, and a one gallon milk jug to hold the water and keep the siphon going.