Reddit mentions of Rockford Fosgate R150X2 Prime 2-Channel Amplifier

Never seen that website before. That would be a bit overkill. The speakers look good tho.

If you're looking to save money you can go with something like this.
Amp
https://www.amazon.com/gp/aw/d/B00BF6HY84/ref=mp_s_a_1_4?ie=UTF8&qid=1502328240&sr=8-4&pi=AC_SX236_SY340_QL65&keywords=2+channel+amplifier&dpPl=1&dpID=510stvQfv1L&ref=plSrch
Speakers
https://www.amazon.com/gp/aw/d/B000P0PF9G/ref=mp_s_a_1_23?ie=UTF8&qid=1502328354&sr=8-23&pi=AC_SX236_SY340_QL65&keywords=6.5+coaxial+speakers

Now if you go that route you'll need an amp install kit. Knu koncepts of very well loved here. I have this same kit in my car.
https://www.amazon.com/gp/aw/d/B005CIJBKK/ref=mp_s_a_1_2?ie=UTF8&qid=1502328557&sr=8-2&pi=AC_SX236_SY340_QL65&keywords=knukonceptz+4+gauge&dpPl=1&dpID=51T-yGZf9YL&ref=plSrch

This will give you plenty of wire for when you add the sub + amp.

Beware of 5 channel amps. In many cases you can find a 4ch (or 2ch) & a sub amp instead.

Bridging & going stereo-only up front is the best way. The problem with a 5ch is that when you bridge & run stereo, you'll have about as much power going to your mains as the sub. A better solution is a 2ch amp + sub amp. (Edit: these are just the fist 2 amps I quickly found that cost about $200 total, other good amps could work too).

FWIW: I have a 5channel amp but will soon replace it with a sub amp & use my 4ch amp bridged for the fronts.

OK, Here is what I would do. This will give you the flexibility to connect a variety of sources.

You will need to get an amplifier that can provide a "bridged" speaker output. A Bridged output will allow you to input a stereo signal (from your chromecast, projector, or other source) and output a mono signal to your speaker. Search Amazon for "Bridged amplifier". You will not need anything too powerful as you will only be driving a single 4 or 8 ohm speaker. This Rockford amplifier looks like it will fit the bill nicely, although at 150W it is probably more power than you need http://www.amazon.com/Rockford-Fosgate-R150X2-2-Channel-Amplifier/dp/B00BF6HY84/ref=sr_1_204?s=electronics&ie=UTF8&qid=1419695728&sr=1-204&keywords=bridged+amplifier

Replace the speaker and wiring, and possibly the volume control. An 8 ohm speaker is standard. Search amazon for "8 ohm speaker", and get one that matches the size of your current speaker.

For the volume control, it is simplest to adjust the volume from the amplifier, but if you want to keep the volume control in the housing, get a single turn resistor that will fit into the same mounting holes. I think this one is probably too physically large to fit, but you get the idea http://www.amazon.com/Single-Resistor-Control-Ceramic-Rheostat/dp/B00JR6GCSW

What I would do is turn the volume control switch into a switch for lights. This is not my area of expertise, but I would go to an automotive stereo store near you as they might be able to make some suggestions for how to mount some LEDs in between the speaker and the grille, and they will probably have a variety of options.

As for the projector, Benq right now is my favorite brand for quality vs price. I have used some of their consumer and professional projectors and been very happy.

Ok i copied some specs of the same exact speakers on ebay.
Any 2 channel would work on these if you're only planning on amping them, but a 4 channel amp would be good for if you want to amplify all 4 speakers front and rear. I would recommend Rockford Fosgate amps, this one is nice. https://www.amazon.com/Rockford-Fosgate-R150X2-2-Channel-Amplifier/dp/B00BF6HY84/ref=sr_1_1?ie=UTF8&qid=1481249591&sr=8-1&keywords=rockford+fosgate+2+channel



Ratings
Impedance 4 Ohms
Power handling 45w rms | 90w max
Technical Specs
Tweeter size 0.25″
Woofer size 6.5″
X-over point 3.5khz
Cone material IMPP NBR surround
Magnet size 90mm x 15mm
Magnet weight 14oz
Frequency response 50hz – 20khz
SPL 88db
FO 50hzMSRP: $249.99

Ebay listing

Normally you spend money on the front speakers and even go without rear 6x9's
That being said you can also save a few bucks on a 2 channel amp to run the just front speakers.

Shoving a pair of 6x9's in the rear dash when you have a 15 inch subwoofer in the trunk can sometimes be counter productive when you can leave the 6x9 rear speaker holes empty to allow the bass to more easily make it inside the cabin of the car.

Considering I have a round about estimate of your budget this is what I would do:

Sub amplifier:
https://www.amazon.com/Rockford-Fosgate-R500X1D-1-Channel-Amplifier/dp/B00BF6HYDE/ref=sr_1_48?ie=UTF8&qid=1468928854&sr=8-48&keywords=3+channel+amplifier

Subwoofer:
https://www.amazon.com/E-12-V-3-D2-Sundown-Subwoofer/dp/B01CZ4M9RA/ref=sr_1_fkmr0_2?ie=UTF8&qid=1468929161&sr=8-2-fkmr0&keywords=sundown+e12+d2

Subwoofer box:
https://www.amazon.com/Atrend-12LSV-12-Inch-Subwoofer-Enclosure/dp/B0013MWT12/ref=sr_1_10?s=car&ie=UTF8&qid=1468929607&sr=1-10&keywords=12+inch+subwoofer+box

Front speaker amp:
https://www.amazon.com/Rockford-Fosgate-R150X2-2-Channel-Amplifier/dp/B00BF6HY84/ref=sr_1_3?ie=UTF8&qid=1468929435&sr=8-3&keywords=2+channel+amplifier

Front speakers:
https://www.amazon.com/Polk-Audio-DB651-Certified-Speakers/dp/B000P0PF9G/ref=sr_1_1?ie=UTF8&qid=1468929479&sr=8-1&keywords=polk+audio+6.5

or if you can spring for a few more bucks:
https://www.amazon.com/Polk-Audio-DB6501-6-5-Inch-Component/dp/B000P0R6LQ/ref=sr_1_2?ie=UTF8&qid=1468929479&sr=8-2&keywords=polk+audio+6.5

You will still need an amplifier wiring kit:
https://www.amazon.com/Lightning-Rockford-Fosgate-Amplifier-Installation/dp/B00PB4BEE6/ref=sr_1_12?ie=UTF8&qid=1468929693&sr=8-12&keywords=amplifier+kit

Why do I recommend this setup?
For the money you are spending and the music you are listening to this will be the best value.

The 15 inch kicker subwoofer you picked is ok but the 12 inch Sundown subwoofer will play lower and hit harder in the proper box. Ive installed both of these subs in the past and the 12 inch Sundown is a phenomenal sub and the Kicker is no comparison.

Subwoofer box:
The subwoofer box you picked out isn't really that expensive when talking about the cost of a quality built sub box. However, the box you picked out is a small sealed enclosure. This will limit the really low frequencies your subwoofer could produce if in a larger box. A lot of the time it is better to opt for a smaller size sub in a larger ported enclosure for producing low frequencies such as rap and dubstep than a larger sub in a small sealed enclosure.

Amplifier:
You picked out two different amplifiers. The sub amp I recommended has a higher rms output rating and better quality components. The amp for the full range speakers has the same better specs. You also picked out a 4 channel amp which is a waste of money when you can get more out of a 2 channel amp. 2 channel amps can still power 4 speakers if wired properly. Although, I would suggest forgetting about upgrading rear 6x9's and upgrade the front stage.

Front speakers:
The front speakers I recommended are some of the best sounding speakers I have installed at their price point. The front speakers are the most important more over the rear speakers because that is where you are setting. I recommended the 6.5 because I believe those are the requirements for your car. If not then opt for the 5.25 of the same line

Note: I am a professional installer with 22 years of experience and have installed more systems than most people ever get to hear in a lifetime.

this amp is what I need to power, I double checked the dyno and it’s 190, I have a bunch of OFC 16 gauge speaker wire and about 6-8 ft of OFC 4 gauge, I was hoping I could use the 16 gauge