Factory stereo upgrade and active crossovers

I recently got a 2011 Prius, non-JBL stock system, no nav. The sound system is... functional... but it's definitely weak at some frequencies and its coloration of music is driving me crazy! I've decided to upgrade in phases, and I plan to install myself. Here's the basic plan:

1. Head unit with Bluetooth
2. Front component speakers
3. Amplifier (probably)
4. Sub (maybe)
5. Rear fill?? (not likely, but it's a thought)

Target budget: <$1000

For my head unit I decided to go with the Pioneer 80PRS. I had originally planned to just use passive crossovers since I've never tuned a system (and a month ago I didn't even know what crossovers were), but then I heard about the 80PRS. I don't mind the learning curve. The unit arrived today, but I'm still waiting for the wiring harness. In the meantime, I've been looking at how to do the wiring. I installed an aftermarket HU in my previous car, but that was 8 years ago.

It looks like the factory HU has 5 things plugged in: front speakers/power, rear speakers, steering wheel controls, aux input, and antenna. Speakers/power will plug into the wiring harness, steering wheel controls will be hooked up to an interface (ASWC-1), aux input will stay unplugged (the aux in on this HU is in the front), and the antenna plugs right into the HU. The outputs on the HU are front/rear/sub OR mid/high/low (active). Note that the active setup doesn't use rear speakers. I'm okay with that.

My question right now is about the front speakers and tweeters. If I'm understanding what I've read, the signal to the front speakers goes first into the tweeters where there is a very basic passive crossover, and then it goes to the woofers. They are wired in parallel, but on each side there are only two wires (+ and -) going from the HU to the tweeter and the woofer. (Based on pictures, there are four wires going into a plug into the tweeter, but two of those lead from the tweeter to the woofer.)

1. Am I understanding everything right so far?
2. If so, is it correct to assume that to do an active crossover, I would need to route an additional pair of wires to the tweeters and do some splicing?
3. The way I imagine it is that I'd connect the front speaker signals to just the woofers, and connect the rear speaker signal to the tweeters. Are there any reasons this wouldn't work (or would be more complicated)? Do you think it would be better to wait until I upgrade the speakers?

 

Thanks for the reply and the info! The HU arrived, and I decided to wait on running wires; for now I just soldered the HU wiring to the wiring harness and plugged it in normally. No active crossover, but there are plenty of other features of this HU to explore. I'm taking pictures of everything so eventually I can share my own install.

Oh, and if you have any recommendations on wire gauges (for when I do run wiring), let me know.