Honestly, to just give the bass a little kick, you don't really need much. I have an '84 Camaro Z-28 (pretty small car) and I have a 600W very off-brand system (could look up the name if needed) system. 2 x 10" subs and 2 x 300W amps. It's perfect. I have them set just right so that they pick up the right bass frequencies and they don't rattle a whole lot...they just "add" to the sound and make it "fuller". I also replaced my stock 6x9s.
So here's my thing; you don't need to advertise that you are driving. What I mean is that OTHER people don't need to hear you. You only need to hear it, right? I think you would be fine with either a pair of 10" subs in an enclosure (or a pair or 12"s). Stay around 500W total and I think you'll have a system that actually sounds decent and doesn't just go "boom boom boom" all the way down the road.
If you are looking to replace the actual mids in your car (the speakers inside your car..in the doors, or sometime behind the back seat head rests), you don't need to add any more power to them. Most newer car output enough power to them to just swap in a set of better quality speakers.
All in all, it will take time to do a project like this (running a hot wire from the battery and running the sub connections from the head unit is the what will take the most time), but if you do it right, you'll be sounding great on a budget.
That's my 2 cents.