Today most zooms that reach 300mm give you virtually the same "reach" on an APS-C camera that we got with a 500mm mirror lens on a film camera, back in the day.
I tried a number of different mirror lenses years ago. I don't recall what all of them were (one was a Sigma... 600mm? another was a really small 250mm, but I can't remember the brand). I finally settled on and for several years used the Tamron SP 500mm f/8. I felt it had the best color and sharpness of all the ones I tried. I didn't try or use the Minolta, Nikkor or Canon (none fit my system at the time), but have heard good reports of all of them. I'm pretty certain that at least one version of Nikkor 500mm f/8 is the same lens, made by Tamron. I had a brief opportunity to compare my lens side-by-side with that Nikkor at a trade show and other than a different rubber grip on the focus ring and a permanently installed Nikon F-mount, they appeared identical or very, very similar.
The Tamron 500mm f/8 is a manual focus "Adaptall-2" lens, with interchangeable lens mounts that can be adapted for use on almost any SLR or DSLR system. There are still many different Adaptall mounts being made, even for systems that come into being until many years after Tamron discontinued the entire line of Adaptall lenses. Just a few months ago I bought an Adaptall for Canon EF-M mirrorless mount, which cost very little and allows me to use a Tamron SP 90mm macro lens on my M5 camera. (I also have Nikon F-mount, Canon EF mount, Konica K/AR, Pentax PK bayonet, Olympus OM and Minolta A mount Adaptalls... which can be easily switched to use any of the Adaptall lenses on any of those camera systems, including modern ones.)
There are two versions of the Tamron 500mm mirror lens: 55B made from 1979 to 1983 and 55BB made from 1983 to 2005. The one I used was the earlier version, which I preferred largely because it had a tripod mounting ring and I very often used it on a tripod or monopod. The later model doesn't have a tripod ring, but supposedly was improved optically. I could never see the difference in images on film. With this lens I would load my camera with Ektachrome 200 slide film (ISO 200), because the other films I used were too slow for steady shots (usually Fujichrome Velvia 50 and Ektachrome 100VS). Modern digital cameras are noise-free enough to use a higher ISO for a faster shutter speed, which might make the tripod mount less important (but if you want it, be careful... it's removable and sometimes is lost).
Another accessory that's important is the screw-in lens hood. It's 82mm in diameter and difficult to replace if lost from the lens. 82mm diameter filters also can be mounted to the front of the lens, if wanted. Or you can fit 30.5mm filters to the rear of the lens. It came with a clear "sky" filter installed there, along with a set of four other filters. One of those was a 1-stop ND filter, though it's rarely needed. Usually the opposite is wanted... more light, not less! The other three filters are colored, for use with black & white film. To install any of these filters, at least on the version I had, it was necessary to remove the Adaptall mount. I rarely did so and only ever used the ND filter on rare occasion. I don't recall ever using the lens with B&W film and the filters for that purpose.
The Tamron 500mm is amazingly close focusing.... to about 5 feet, if memory serves.
I also thought it handled backgrounds better than most. Specular highlights in out of focus areas tend to show up as "donuts" with mirror lenses. It has to do with how the light path through the lens is "folded" back to the mirror in the center of the front element. I always felt the Tamron somehow managed to minimize this effect. All the images below were made with that lens. Particularly in the shot of the egret, you can get some idea how the Tamron lens renders "donuts".
The orange canna flower above gives you some idea how close the lens can focus, as well as how strongly it can blur down backgrounds. This actually wasn't even all that close, the lens can get much closer. I think it can do about 1:3 magnification, or about 1/3 life size. (So an object approx. 3" x 4.5" would completely fill the viewfinder of a full frame digital.) About 15 or 20 feet behind the flower there was a fence, which is obliterated into a blur here.
There is no means of controlling depth of field with most mirror lenses. Their aperture is fixed (in this case, f/8). Exposure in most cases is only "adjustable" with ND filters, which have no effect on DoF. (Two exceptions were Reflex Hexanons made by Konica: a 1000mm f/8 and a 2000mm f/11. Those lenses have a set of Waterhouse stops in the rear that can be dialed into place to change the aperture. They also were unusual using a bellows focusing mechanism behind the lens. The 1000mm was pretty big, but the 2000mm was massive and weighed about 35 lb. AFAIK, none of the 2000mm were sold and only two were ever made. I saw one at a photo fair in Denver in the 1980s. Supposedly there was one on display in the Konica-Minolta headquarters when Sony bought their photography division in 2006. There were some several dozen or couple hundred of the 1000mm sold new for about the price of an economy car in those days and they still show up for sale used occasionally, but also still bring big $.)
The Tamron 500mm f/8 is fairly common on the used market and can often be bought in good condition for $200 or less. The Adaptall I bought most recently (for Canon EF-M) cost me under $20 shipped from China and arrived in about 5 days. A more advanced "chipped" Adaptall I bought some years ago (for Canon EF) was more expensive... about $35. (The "chipped" adapters allow Focus Confirmation to work on the DSLRs... that's not needed with the Focus Peaking in the mirrorless cameras). That also came from China and quickly delivered. Adaptalls are easy to find used in a number of vintage mounts and are still being made brand new for modern mounts.
There also is a much less common Tamron SP 350mm f/5.6 (model 06B, I think). That mirror lens tends to sell for much more due to it's relatively rarity. It's much smaller than the 500mm and a very nice lens, too.
Tamron also offered Adaptall-specific teleconverters: 1.4X and 2X. Those fit between the Adaptall mount and the lens, so that it's not necessary to buy another mount. I experimented with the 2X and with another brand 1.5X and found the loss of image quality too great. I don't recommend using teleconverters with this lens at all.
Ultimately I sold my Tamron 500mm when I found a 300mm f/4.5 (standard lens, not mirror) and 1.5X teleconverter combo that gave equally good image quality and was more versatile (two focal lengths: 300mm and 450mm... instead of just 500mm).
Frankly, most modern lenses in the 400mm, 500mm and 600mm range... even zooms... can match or beat the old mirror lens' image quality. A 300mm on one of my Canon APS-C cameras gives me essentially the same "reach" that I got with that 500mm on my film cameras. Of course, using the 500mm on an APS-C would make it "act like" even longer.... equiv. to 750mm or 800mm on full frame. However, the high density of recent APS-C camera sensors is pretty unforgiving of lens shortcomings and even very slight camera shake. Expect to use higher ISO to be able to use 1/1000 or faster shutter speed, if you plan to hand hold the lens.