... now I just need to find the easiest and best way to control them. I was looking for different types of controllers for the automotive use but I think my best bet is to go with an Arduino uno board. I just don't know the first thing about writing code for this at all.
Baby steps.
The Arduino kit you've nominated has a Tutorial. I have no idea whether it will be good or bad - but I would suggest you start off by running through that tutorial on your own. Having been a mechanic, you will have learned how to be logical and methodical - so just step through the tutorial, making sure you understand each step before moving on. If you get stuck, you can always bring your questions here.
The LED panel you have chosen is not a bad choice. It has the control electronics for each pixel built in and all you have to provide is power and a signal.
The power requirements for the LED panel are 5V at up to 4A (when every pixel is at maximum brightness)
per panel, so you will need a 12V to 5V power unit capable of 8A or two capable of 4A. The two unit option would be my preferred solution. You could keep one close to each panel (reducing the distance 5V has to travel is a good thing). Also, it might be wise to consider a unit designed for vehicular use, because automotive power isn't renowned for being well behaved.
The signal is a something you won't need to know too much about, since there are routines already written by others that take care of that. The FastLED library for Arduino seems to be a popular choice. You only have to worry about passing on the information as to how you want your LEDs to be lit
BUT don't worry about that just yet. Get your Arduino and run through the tutorial. Try a couple of programs (the Arduino crowd calls them 'sketches') and then try something simple of your own design.
Don't be tempted to get stuck into the LED panels too soon. Programming is like learning to drive. You haven't got your 'L's yet and programming the LED panel is like rally car driving. Don't try getting ahead of yourself or you might crash and burn. On the other hand, you might find yourself with a natural talent, in which case all we will need to do is point you in the right direction and you'll take to it like a duck to water.
One thing that you will find is that there are many examples of Arduino programming to be found on the internet. Developing your Google-fu can prove very useful here. Some of them are not wonderful and others are truly brilliant. I'm sure you've encountered similar things in other areas of life, so you will know what I mean. With programming, though, you can have a progeam that is not written to the best standards - but it will work well enough for the purpose ... and because the ugliness is hidden inside a silicon chip, it can live a full and productive life, devoid of criticism. Often these shaky lives are in a commercial environment, yet they hang on well enough for their creators to be kept in employment.
The bottom line is - if you find something that works well enough for your needs, you don't really
need to rewrite it or polish it up or change it in any way. It's like a kludge in the engine bay of a car - if it works safely and reliably, just don't look under the bonnet and nobody will be the wiser.
Anyway - for now, just get your Arduino kit, run through the tutorial and see how you go.