It sounds like you're on the right track. (Except an Impreza isn't very powerful. Could you be thinking of the WRX?)
The main downside of the Mazda3 is that its back seat is somewhat tight for the class.
So is the back seat in the Ford Focus, but otherwise I'd recommend one IF you'd be buying a manual. The dual-clutch automatic has been troublesome.
Two that aren't quite as fun to drive as the Mazda and Ford, and that aren't quite as fuel efficient as the SKYACTIV Mazka, but that are roomier, are the Hyundai Elantra GT (based on a European-market model, not the Elantra sedan) and Kia Forte5. Both are worth a look, especially if you can find one at an attractive price.
Then there's the Ford C-MAX, which could be the best fit of all for your needs. Same powertrain as the Ford Fusion Hybrid, but a hatchback.I liked driving it more than the Fusion, and far more than the Prius. Really good handling for a tall hatchback. My suburban mpg was in the high 30s. The 2013 required repairs for common glitches initially, but recently have a repair frequency just a little worse than average, but the 2014s have been very good so far. They're pretty cheap used. 2013s are pretty easy to find with under 45,000 miles and under $12k. A 2014 might require $14k, but could be worth the difference if you can afford it.
In general compact car prices are low right now, probably owing to cheap gas.
You'll find links to detailed reviews beneath the photos.