6 or 10 speaker system on a budget?

Without going into the realm of brand names, here is what I suggest:  get rid of or disconnect ALL of the OEM speakers.  It never matters how many speakers the car came with.  Replace the deck with one that has at least one full-range preout and one sub preout.  Use two sets of speakers in the cabin and one 12" subwoofer.  Use a four channel amp and a mono amp.  The fronts should be 6.5" component sets and be placed in or near the doors;  the rears should be coaxials and be placed in the rear deck in factory locations.  The rears should be faded much lower in volume than the fronts.  The sub can be placed wherever you choose.

Use the search  function above this page to find more info on setting up a system, starting with a search for "gain".

Use the amplifiers for crossover functions between the speakers and the sub.  The components and the coaxials will have their own crossovers to separate freqs to their drivers;  you just need to set the high pass and low pass filters on the amps and use the deck how you see fit for final fine-tuning of the sound.  80 Hz is a suitable crossover freq for the transition from sub to mains, and the front and rear sets of speakers WILL be playing the same frequency range.  It is the adjustment of the fader that will bring out the more important, and better quality, fronts.

Include in your budget as much as possible for Dynamat or an equivalent damping material.  It is crucial in quieting the sheet metal noises that will suddenly occur when you power up a real sound system.  There cannot be happiness until this is done, and it's best done at the same time you have the car apart for the install.  If you are careful and a good shopper, and have the capacity to do most or all of the work yourself (including building the sub enclosure), you can put in quite a nice system for a relatively low outlay of cash.   $700 to $1000 or so, depending.  And more is, of course, better. 

And for a lower cost, you can start the system with coaxials in the front and leave the rears out of the picture.  Then when you are able to upgrade, move the coaxials to the rear, buy a set of components for the front, and then you can employ all the channels of the four-channel amp.  But if you go this starter route, do the wiring and damping as if you were installing the complete system...so you don't have to buy new wires and fuses and tear the car completely apart again.

Use quality amplifiers.   and that's about it for my input  ;)