I agree with stephent's question : "Is it a boiler or heater?"
If it is a boiler, I'm not much help. If it's a wood fired water heater, I can help. I work at Woodmaster on the assembly line of the outdoor woodburning and cornburning water heaters.
If it is a firebox inside a waterjacket style heater, you generally insulate them on the outside with standard unfaced fibreglass insulation, exactly like you use on the walls of your house or the attic roof. They are then sided with some form of metal or ABS siding to help protect the insulation and for beautification.
It is not required to insulate them if they are being kept inside another building. Since the absolute hottest a regular wood fire will get the water is 212 degrees F (100 deg C), there's not much chance of it lighting anything on fire by contact. So long as it has a water level sensor (plunger style) to warn you of a low water condition. Also you'll want to vent the overflow pipe outside so as to reduce condensation accumulation in the shed as these things quite often can boil off up to 10 gallons in a day if they run too hot.
The easiest and most cost effective way to insulate the Pex tubing is to stuff both the supply and return lines inside a 4" PVC pipe and insulate the outside of the PVC, generally with some form of styrofoam type insulation. You can buy the pipe specifically designed for the purpose, but from what I've found it's around $5 -$7 a FOOT!! Set the PVC pipe in the trench and surround it with pea gravel. Then bury the lot of it with dirt. You want to get at LEAST 6 inches below the frost line for your area, preferrably 12 inches below. For me that meant digging a 4 foot deep trench and hoping for the best as the frost line around here CAN get down 6 feet.
Woodmaster uses the Taco brand of pumps, specifically the 007 and 0011 models. They are 20 and 28GPM respectively with zero head. I personally think that's a little low, so I went with a 1/2hp pump from Harbor Freight. Maybe a little overkill, but I'll never have cold spots with it.
If you have any more questions, feel free to ask. I'll either be able to answer them myself, or I can get the answers on Monday when I go to work.