I've picked up Runner a few months ago. I was already looking to upgrade the speakers prior to finding out the previous owner has already done some work. I currently have the Infinity Kappas in the dash and the rear hatch. I am looking to incorporate some of the stuff I already have lying around or selling it to purchase other equipment. Here are some of my options

Fronts
I've had the MS-62C in my BRZ and liked them but I've heard alot of good thing about these others as well.
JBL MS-62C (Currently Have) OR
Image Dynamics CXS64 v.2 OR
Dayton Audio RS28F-4 1-1/8" Silk Dome Tweeter and Dayton Audio RS180-8 7" Reference Woofer

Amplifier
I ran the MS-62C using the Alpine MRV-F300 and it does the job well. Also the Alpine MRD-M605 was used for the JL Audio 10W6v2-D4 in another previous car and it has no problem kicking it around
For Fronts
Alpine MRV-F300 (Currently Have)
For Sub
Alpine MRD-M605 (Currently Have)

But I am seriously considering the idea of a 5-Channel Amp to save space since I'd like to keep the interior looking stock and this would also use less wiring
Alpine MRV-V500 OR
Alpine PDX-V9

Subwoofer
Awesome sounding sub and not sure I really want to part with it for something smaller
JL Audio 10W6v2-D4 10" Dual 4 ohm W6v2 Car Subwoofer

Processor
I used the AudioControl LC2i in BRZ but it also had a far superior headunit and debating on going down the rabbit hole with TacoTunes ReCurve EQ. The Runner's Headunit output is all over the place and lacks even basic adjustment.
AudioControl LC2i (Currently Have)
TacoTunes ReCurve EQ or Equivalent

Yours is non-nav right? I have a 5 channel amp and a LC6i running to my 14+ entune head unit and it takes some fine tuning but it does the job well. The rest of my system is lower-end than what you're installing, so it will sound even better I'm sure.

That being said, I can understand why you'd want to add a sound processor. The stock head unit leaves a lot to be desired, and I'm sure it's the same with the pre-2014 versions. I'm seriously considering a DDX9903S | eXcelon | CAR ENTERTAINMENT | KENWOOD USA for a number of reason. 1. It has 5v preouts, so I would be able to eliminate the LC6i as well as a bunch of wiring, by running RCA's directly to the amp 2. It has a capacitive touchscreen which is the best on the market right now (somewhat imo). 3. It has CarPlay/Android Auto 4. It's also compatible with the Maestro system to integrate with the stock camera/steering wheel controls etc. AND it also adds a bunch of features. For example it can pull vehicle diagnostic info to show all kinds of temps and pressures and top of that it will show the actual tire pressure for each wheel instead of a stupid light that means ones of your tires is low, but we're not telling which one. The one downside is that with the Maestro unit and the install stuff it's over $800. Bonus: It also supports a front facing camera that you can view while wheeling.

I'd be very interested in your Kenwood install as am looking to doing the same thing. Not sure how it'd fit in the dashboard though a double din is supposed to be standard. I think there was DIY someone else did awhile back on the wiring.. Keep us posted!

I did a lot of research on this before making a decision. First, I installed dynamat and new speakers. Then I installed a Kenwood compact sub. Then I installed a new head unit, the Kenwood DDX9903s.

Here are some helpful posts...
Speakers and sub:
Speaker replacement & Sub addition

Other speaker and sub discussion:
Speaker Replacement Opinions

Aftermarket head unit discussion:
New Maestro Radio Solution

My experience with the Kenwood DDX9903s:
New Maestro Radio Solution

Hope this helps

BTW: the head unit fits perfectly in the dash. Wiring was unbelievably easy.

Yeah I'm non-nav. I would love to drop in a new headunit but my issue is I'd like to keep all the factory utilities steering wheel controls, USB, bluetooth mic and antenna. As far as I can tell keeping the bluetooth mic requires some hacking and adding SAT radio meaning running another antenna.
Also with the sound processor I kinda feel like a need to get one. Because no matter how much you spend on speakers and amplifiers your just going to get a crisp shitty signal.

You don't have to run a new antennae for satellite or GPS. The idatalink Maestro will allow you to keep all steering wheel buttons and you can even program them to more things. Running the mic from the new stereo literally required removing one bolt in the a-frame panel. You keep the factory USB port. I bought through crutchfield. The price was a bit higher than going through Amazon, but crutchfield provides instructions, phone help, and a database that tells you exactly what you need. There are tons of videos by tacotunes on YouTube about removing the stereo, running subwoofer wires, etc.