First, I'm not fond of ring lights for portraits, in most cases. I'm just not fond of the catchlights they produce. My personal preference for portraiture is one of two lighting methods. Studio strobes with modeling lights or LED lighting, such as:
https://www.bhphotovideo.com/c/product/1302652-REG/smith_victor_401608_750_watt_led_2.html
https://www.bhphotovideo.com/c/product/1323079-REG/savage_led60k_r_savage_500w_led_studio.html
Those allow for more precise, no guesswork, setups.
--Bob

I had a brief demonstration (class) of lighting and portraiture, and found that ring lights can be awesome tools. Once you find the right angle, distance, luminosity, etc., the results can be striking! If I were in the market for a ring light, I'd look for one that has adjustable color temperature (that would address the incandescent vs. fluorescent question) and would probably opt for the 18", since I think there's more flexibility with that setup. The 14" might do given your requirements.

One thing I have noticed is that the catchlights in a person's eye are often reflecting the ring, and unless you can deal with that "oddity," you might want to prepare for some post processing to make the catchlights look more natural.

With a wide angle lens, you don't need f/2.8... let along f/1.8. In most situations, a large aperture serves no purpose. Short focal lengths are relatively easy to hand hold steady at slower shutter speeds, so a big aperture is less necessary for that. Plus wide angle lenses have great depth of field, most people end up stopping them down for even more most of the time, and it simply isn't possible to blur down backgrounds very much. So there's little reason to want a large aperture lens for that reason, either. One exception is astrophography... folks shooting at night might want a larger aperture for a brighter viewfinder. Photojournalists may want one, too. In fact, very fast, wide lenses often have lower image quality than less extreme designs. Often they are less sharp at the corners and have more chromatic aberrations, coma or other anomalies.

All that said, the best priced wide angle for your camera is the Canon EF-S 10-18mm f/4.5-5.6 IS STM that costs under $300. It's a bit plasticky, but for hundreds less than most lenses of this type, what do you expect? It's one of the most compact and lightweight (uses 67mm filters), got very good image quality considering the price and also one of the few with image stabilization (further enhancing it's hand-holdability, though IS probably isn't as important on a wide lens, as it is on a telephoto).

If you want a better built lens, the Canon EF-S 10-22mm f/3.5-5.6 USM sells for around $600 and has some of the best image quality of any ultrawide. It's a bit heavier and larger, but not bad (77mm filters). Note: neither of the Canon lenses come with lens hoods. Those are sold separately for about $20-$25. Highly recommended, though. While the lenses are pretty flare resistant on their own, the hoods make them even more so. The hoods also help protect the front element from bumps and are worth buying.

If you still want a faster lens, the only ultrawide with f/2.8 is the Tokina AT-X 11-20mm f/2.8 DX. It's sharp and popular for astrophotography, costs about $500. Comes with the hood. Like most (all?) Tokina lenses, it uses a "focus clutch" mechanism where you shift the focus ring forward or backward to switch back and forth between manual and auto focus. Because of this arrangement, the Tokina don't have "full time manual" override, like the Canon do. The Tokina also rotate their focus and zoom rings the opposite direction from Canon (i.e., the same direction as Nikon). I use a Tokina lens and haven't found these things big deals, out in the real world. The 11-20mm is one of the larger and heavier UWA lenses.... uses 82mm filters.

Tokina also offers an excellent AT-X 12-28mm f/4 DX. It's a little smaller, lighter (77mm filters) and less expensive than the 11-20mm. Usually about $450, I see it's on sale at B&H right now for $250. That's a great deal!

Sigma offers a couple ultrawides. The Sigma 10-20mm f/3.5 DC has come way down in price, to about $450. It used to be one of the most expensive. It's also one of the heaviest and largest (82mm filters). There's also a Sigma 8-16mm DC, which is the widest of the wide angles... interesting lens, but it has a lot of wide angle distortion and cannot be fitted with standard filters (due to a protruding convex front element). Usually costs more than most at $600, too. Sigma 12-24mm DG can also serve as an ultrawide on your APS-C camera, but it's a more expensive, bigger full frame lens that would be largely wasted on a crop camera. $950, some wide angle distortion and can't be fitted with standard filters.

Finally, the Tamron 10-24mm f/3.5-5.6 Di II VC has recently been redesigned and had stabilization added. I don't know how it compares but it costs about $500.

All the third party lenses come with matching lens hoods.

I use the Canon 10-22mm and consider it one of the very best from any manufacturer. I've also used earlier Tokina ultrawide models and found them excellent and "L-like" in build quality. When I tested earlier Sigma 10-20mm (variable aperture f/4-5.6 version) and Tamron 10-24mm (non-VC version), I was less impressed with them. But I've seen folks get very good shots with them.

Have fun shopping!

I would seriously consider Alan's advice here. Personally I doubt that you need a large aperture ultra wide for this work with a Canon 80D. You say you want black backgrounds, or at least controlled, and will be using flash or other lighting. The Canon EF-S 10-18 is well worth considering unless you intend to physically abuse it. I have the EF-S 10-22mm, which is about twice the price, but the 10-18mm wasn't available when I bought it. Highly recommend the EF-S 10-22mm from personal experience.

That said, almost any of the recommended lenses would do a decent job, I suspect that lighting will be a greater challenge...

What lights do you have, or are you considering? How experienced are you with lighting?