Read your shock manual. Mine requires that it be repacked with the proper type of grease, because certain grease types will degrade the bushings.
For chains in wet conditions, you want a fairly resiliant lube. Normally greases are not advised because they pick up sand, but if you're going to be getting your chain muddy anyway, greases are probably best. Remember to remove and completely clean and dry your chain before you re-lube it. Most people use a chain tool and a dish full of degreaser for this purpose.
Remember to always check chain wear when you clean your chain. If its worn more than 0.5%, you need to get a new one pronto. Otherwise, you'll probably be buying a new cassette soon as well.
What sort of lubricants are you considering using? I tried using CLP for a chain once, and it majorly did not work. It was just too light for a chain. However, I do use CLP as a light lube for other parts of my bicycle.