Ok, for starters, your headunit will be around the 4x50 mark (4x18 - 23 rms)depending on the model. As for throwing some 6" in the front, i dont think its too much of a hassle, but i dont remember if a spacer or similar would be needed. The door trims are pretty easy to get off from memory, i just dont remember a step by step rundown ( sorry, not being much help here). You should be able to use the the factory wiring as i dont think the LX had the primo sound system, therefor no factory amps (someone correct me if im wrong here).
A decent "budget system" would entail a half decent set of front speakers (splits), a half decent 4 channel amp and a half decent 12" sub in a box. Basically, use the amp to run the fronts, and brigde the rear channel for the sub, run the 6x9s off the headdeck, this will give you a pretty good sound for the $$$ (although depending on your definition of "budget" this may change)
Any other Q's, just ask