For better, but not ULTRA car audio, I recommend my own path, the one I recently took with my old Accord.
Craigslist or Kijiji for the head unit - I sourced a 2 year old Pioneer that does everything you need, for $120 installed.
I then turned to eBay for the speakers, and in my case amps.
I bought new, but aged in the box, high end separates - in my case Zapco, but there are Alpine, Focal and MB Quart on there all the time.
I also bought used amps on eBay, but stuck to high end brands used - I bought a late 90's Orion, and an early 90's PPI.
All in under $500.
For a new, simple setup, I would honestly consider new from Best Buy or Future Shop for a head unit, and get them to install it.
Speakers, it is hard to recommend coax's, though for the application you suggest, it will likely do.
For the hatch - are there speakers in stock locations back there?
If so, upgraded ones, and the use of a 4 channel amp might prove useful, especially since so many now include crossovers for each set of channels. You could use one set of channels for the front speakers, and high pass them where they sound their best. You could then consider running the rears (hopefully 6x9's) low passed, in mono, in parallel, simply as baby subs.
I bet your wife would like the added, but not overwhelming bass, and the stock locations leave you wide open in the hatch for utility.
Good luck, there are tons of quality used car audio options.
Stick with high quality used speakers, and I bet your budget is easy to stick to - now that IS rare in audio!