Since you can buy just about any part of a Weapon Carrier, and lots of good repro stuff is available from the like of Midwest Military, there are no showstoppers when looking for one to buy.
In general, though, completeness. You don't really want a cab and chassis, so if it doesn't have the correct intact body, move on. It is nice, though not essential, to have the correct engine code - T202, T207, T211, T215, T214, or T223.
Canvas and tyres can be expensive, so if you were choosing between two otherwise similar trucks the one with the best canvas and tyres would save you some money.
Personally I would always buy a winch truck, rather than a plain front, but I'm sure others here would have exactly the opposite opinion.
Final thought - when looking for a Weapon Carrier, you might run across a good deal on another Dodge - Command Car, Carryall, Ambulance, Maintenance or Telephone truck - give them due consideration. A Command Car or Carryall will always sell for more money than a Weapon Carrier, but again if you buy either of those completeness is even more important as parts - original or reproduction - are rarer and more expensive.