Thanks, overall a good introduction. But I need to point out a couple of things that would otherwise trip up newcomers.
First, you use the incorrect term “Model 3”, which can lead to confusion between the Tandy Color Computer 3 and the TRS-80 Model III.
The RadioShack TRS-80 Model III, introduced in 1980, was an all-in-one machine that contained the computer, a keyboard with a numeric keypad, a 12-inch black-and-white computer monitor, and slots for two 5¼” floppy disk drives. While it had some limited game capability and some games were sold for it, it was mostly intended as a practical tool for business, education, or home users. Here’s a Model III:

The Tandy Color Computer 3, introduced in 1986, combined the computer and keyboard into one unit, with any display or disk drive used being separate machines connected via cables.
Here’s a typical CoCo 3 setup:

Although the two machines were usually compatible with the same hardware peripherals, especially those from RadioShack, such as computer cassette recorders, printers, plotters, modems, external hard disks, and more, they were NOT at all software-compatible owing to having CPUs from completely different hardware families. I would hate for someone to buy a Model III game expecting to be able to run it on a CoCo 3, or vice versa.
The key error is in your use of the term “Model”
as part of the computer’s name. While using the word as just a word can be correct, such as “Tandy then released a new model of Color Computer, the CoCo 3”, it is not correct to actually call it the “Model 3”. The word “Model”
as part of the actual name of the device is not only not part of the official name of any Color Computer, it was also never even used unofficially by any part of the CoCo community. The word “Model” in the name of a TRS-80 computer can only refer to a computer that is NOT a CoCo.
Second, newcomers, especially those who plan to use the actual physical computers and physical cartridges/tapes/disks, need to know that while the CoCo 3 had greatly improved graphics capabilities and was largely compatible with CoCo 1 and 2 software, there were two major exceptions to this software compatibility which were especially common with games. And I’m talking
exceptions that are BEYOND the copy-protection schemes you mentioned.
The
first compatibility problem came from a relatively rarely-used mode in CoCo 1/2 games called
“semi-graphics mode.” It usually had very low-resolution blocky graphics, but had the advantage of being easy to program, having many colors available, and being able to be interspersed with standard CoCo on-screen text without additional programming effort. It was used most often in the very first years of the CoCo’s existence when available memory was very modest (4K), many programmers were using BASIC rather than having mastered CoCo machine language (although some semi-graphics games used ML), and the full capabilities of the hardware had not yet been fully explored.
"Pac_Tac", a Pac-Man clone:

"Storm", a Tempest clone:

"WormTube", an original arcade game somewhat like Defender or Vanguard:

The Coco 3 simply cannot do this and cannot run these games. It’s a real shame but at least there aren’t too many commercially released games that used this mode in the game itself, perhaps a couple of dozen.
However, even as the 80s rolled on, semi-graphics mode continued to be used a lot, not so much in the actual games, but in their title or intro screens. Again, a shame, but fortunately this time it’s not a total compatibility-breaker. So if you buy and load a game that’s supposed to be CoCo 3 compatible (does not say “CoCo 1/2 only”) and the title screen looks odd or jumbled, check the instructions to see what the program expects you to do to get past that screen (such as typing your name, selecting “1” or “2” on the keyboard for the number of players, etc., and do that to get past the title screen. Then the game should work.
The
second compatibility problem came from the fact that even though the CoCo 3 fully supported the original CoCo’s hardware-supported official color sets, those sets were a bit TOO colorful, with color schemes that were not very desirable or useful and were therefore rarely used especially after the first few years of the CoCo.
The first such official colorset had the colors green, yellow, red, and blue, which sounds fine, but the catch is that it had to be on a blazing nuclear/neon-green border and background. This was fairly commonly-used in the first few years of the CoCo, especially by RadioShack itself.
"Lunar Rover Patrol", a Moon Patrol clone:

"Tennis":

The second official colorset had a white border and background and the colors white, cyan, magenta and orange. Almost nothing ever looked good in this eye-blearing pastel mode and it was very rarely used by any game publishers.
"Cuber", a Q*Bert clone:

"Chatwin Manor", an original adventure game:

"Bagasaurus", an educational title fromthe Children's Computer/Television Workshop which owned Sesame Street:

Again, these color schemes work with the CoCo 3 with no problem, but programmers, especially those outside RadioShack, and after the first few years of the CoCo, rarely used them.
Instead, the vast majority of CoCo 1 and 2 games use a programmer’s trick called
“artifact colors” that take advantage of a quirk of the era’s North American hardware and software to produce what looks, on a TV set (the CoCo 1 and 2 were designed and intended to ONLY use a TV set as their “monitor”), like a much more normal and useful four-color scheme: black, white, red, and blue, with either a black or white background, and in a decently high resolution of 128x192.
"Donkey King", a clone of Donkey Kong:

"Sailor Man", a clone of Popeye

But, the trick to produce red and blue this way on a TV set does not work on a CoCo 3 which is (as intended and designed) sending an RGB signal to an RGB monitor. The trick produced red and blue by sending tiny white dots on a black background to the TV set, but on the higher-resolution RGB monitor used by the Coco 3, the result was
simply a black-and-white image. I still shake my head that Tandy didn’t bother to include a feature to detect and “translate” this trick into actual red or blue on a CoCo 3 using RGB. This huge oversight forced many CoCo owners into the decision to either have TWO CoCos on their desks with TWO different screens, or to have to give up having color for the majority of their classic CoCo 2 games when played on the CoCo 3. And it’s not like the artifact trick was strictly done by third parties. RadioShack themselves did it with games like "Clowns & Balloons" (a clone of Circus and Circus Atari)

and with the official port of Zaxxon:

So, bottom line, your choices are:
One, rely on emulation with a modern PC, avoiding the problem entirely but missing out on the fun of using real hardware.
Two, use a stock CoCo 3 and RGB monitor (like Tandy’s CM-8 which was designed and intended for the CoCo 3) while understanding that semi-graphics games won’t work, semi-graphics intro screens will glitch, and CoCo 1&2 games that use artifact colors (as the VAST majority did) will be in black-and-white.
Three, use a CoCo 3 that is somehow hacked or modified to overcome the above problem.
Four, as you mentioned, get BOTH a CoCo 2 outputting to a TV set AND a CoCo 3 outputting to an RGB monitor. You’ll either also have to get duplicate disk drives and perhaps multi-pak add-ons, or in a very cumbersome fashion disconnect your only multi-pack and disk drive from the CoCo 2 to connect it to the CoCo 3 when you want to play CoCo 3 games, and vice versa.
I don’t want to sound like a downer! The CoCo was a great machine, the games were terrific, and it was all huge fun. I just want newcomers to know what to expect and not have an unpleasant surprise.