I'm pretty new to the Vette world, but I too have a '90 coupe. It used to have the bad bose system with the tape deck. heres what I did:
Went to best buy and bought:
1x Dual 220 Watt system. 3 knobs flip screen. not mp3 compatible=$150.00 (it saved me $100.00+)
2x Alpine 6 1/2 inch. speakers for the back.(not 6x9, wont fit well)
2x Dual 4 inch in the front I believe.
Bought the alpines without the box for a discount at $70.00 i think. duals were like $40.00. and the system itself was 150.00 about.
so thats $260.00. It cost me $100.00 even to install once they figured out how to take the panel off they cut a black peice in the back so my particular system didn't stick out. Make sure they do the speakers to so they can rewire the car. Then they added a 3 cd case holder on the bottom to fill that giant bose space. The flip screen has about 1 millimeter of clearance when out and in park. Just barely made it, but i couldn't be happier with my system. It has all the bass I need and I didn't need an amp/sub. The flip screen LCD display makes it look high-tech and the red lighting meshes well with the A/C orange and other interior lights.
Because I lived quite a ways from Lombards Auto Center in San Luis Obispo, I couldn't get this done very quickly. This is why I believe they gave me a little discount. but still, this setup is way under $600 and The sound is awsome. First thing my friends said was: "wow that sounds really nice!". They all said that when I showed the 5 friends individually. However, i couldn't get the Dual system to raise the antenna. Seemed to recieve radio stations perfectly without it up and I never really liked the look of the antenna. I just got it done this morning and I have gotten so many compliments!

I couldn't be happier. Good luck with that bose system, I wish I knew how to get pics on here

sry.
I'm not an expert, but thats my opinnion.