Ah, weapons == shells, so to speak. I refer to it that way because buying/finding the same weapon twice doesn't change anything but the ammo count.
Without spoiling too much... it is impossible to keep your original weapons the ENTIRE way through the game, even if you completely avoid being killed or busted.
The missions are actually one of the easier parts of 100% completion. For my money, the toughest parts are finishing the Ambulance missions (it's about forty minutes to finish level 12, and you have to do it in one continuous run in the same Ambulance -- no repairs possible) and the Rampages. Some of the Rampages will simply make your brain hurt.