Hmmm, I have heard of the same problem recently. It would be a shame to bypass the excellent Bose system but if you must, here are my thoughts.
Well if you want to set up a system including a sub I would look at getting a decent headunit with 3 pre-outs.
That will have outputs for front speakers, rear speakers and a sub. All can then be controlled via the head unit.
The purists don't like this, but for most of us this is the ideal solution.
Headunit should be a known good make.
Pioneer are generally regarded as doing the best around right now. Right alongside them are Alpine.
Other good units are made by Kenwood and JVC.
Nothing wrong with buying a good second hand one. If doing this you will get much more for your money.
These 2 units are very highly recommended!
Pioneer DEH-P8600MP (got one here best I have ever used!)
Alpine CDA-9835R.
Pick either of them and you won't go far wrong.
Amp. Well 4 channel (4x 30-40w RMS) is ideal. Look only at the RMS figure, ideally at 12v. This is the only real measure.
You don't need more than this amount of power for the door speakers.
Buy amps from Alpine (old V12 seies are wonderful), Pioneer, Kenwood, or Phoenix Gold. Again second hand will get you excellent value for money.
Sub I would run off a seperate amp just for that job.
"Active" subs are an easy and very effective solution. These have the Amp built into the casing of the sub so they are matched up.
Take up less space and are very effective.
Infinity Basslink (I had one, impressive) and Vibe CBR 10 (or 12) are the ones to go for.
Wiring it all up should be quite straightforward, but I have never tried to tap into a Bose system so I will say nothing more than that right now...
Power supply to rear of car is easy. Standard 5m cable really is not long enough though. Try and get at leat 6m fused power cable.
Run from battery, through the 2 rubber grommets on passenger side, through the bulkhead into the car, down past glovebox (remove for ease) under passenger kick plates and past rear seat into the boot.
It may seem like a lot of work (and to be honest I would rather discover issue with changer) but the end result is well worth it!
The job is not hard, but it will take some time. Plan ahead, make sure you have everything you will need, know where you are going to fit everything and be patient.