Hello Commander Stryker and welcome to the forum!
I have some good news for you... almost everything (95% or more) is already doable today.
Somebody (you?) just needs to do it.
The idea for using Hero Units is that these special soldiers have their own custom sprites, weapons, and armor. These Heroes would all start out at the same rank that any other XCOM soldier does, but they start with slightly better stats than your typical rookies.
Own sprites are doable, own armors are doable.
Own weapons are doable (as a fixed part of own armors).
They would start as rookies and could go up the ranks.
They can start with better stats (defined as a new soldier type), they could even gain stats quicker than normal soldiers.
Here are some ideas on how you could recruit a Hero:
1. Whenever you recruit new soldiers or start a new game, you have a random chance of getting a Hero
2. You can recruit Heroes from by purchasing them from their own pool but its more expensive to do so as compared to recruiting
3. Just have every single Hero soldier as a one-time purchase for each specific one
1. already works this way
2. already possible
3. this is not possible in vanilla, but is possible in my extension (OXCE+), you could "manufacture" them from limited resources
On the subject of weapons and armor, each Hero would have their own special equipment. Some of their weapons could resemble standard XCOM weapons but have special names and can only be equipped on the Hero it belongs to.
Yes, this is how fixed weapons on armor work.
And since you have to research better weapons for your normal soldiers to use against the beefier aliens, why not add some new research projects that allow you to upgrade the armor and weapons of all of your Heroes. For example, after successfully researching Laser Weapons, you unlock a new project called "Heroic Laser Weapons" or something of that nature which would unlock laser weapons for your Heroes specifically.
Yes, doable.
Heroes would also have some kind of special icon on their stats and/or inventory screens to tell the difference between a normal XCOM soldier and a Hero. And, the best part is, these Heroes could be anything from your favorite '80s action heroes to your favorite cartoon character or they could even be some crazy version of yourself.
In geoscape, you could tell them apart by having their unique armors and/or unique names (from a different name pool than other soldiers).
With OXCE+ extension, you could even have nice small armor preview icons.
In battlescape, if you would use my OXCE+ extension... you can even see their FACES (instead of rank)... so you can see the portrait of your favourite '80s action heroes at all times.
Good luck with the experimentation!
Share your work, if you decide to mod any of this.