One of the least expensive, reasonable quality telephoto solutions is a manual focus "mirror" lens... but there both good and bad examples of those, too.
Over the years, I've used a number of different mirror lenses. The one I liked the best of all is the Tamron SP 500mm f/8. All the following were shot with that lens:
Notice the round "donut"-shaped out-of-focus highlights in the background of the 1st and especially the 2nd image... That's typical of mirror lenses, due to their design. IMO, the Tamron 500mm handles this better than most, that the donuts are minimized and not too distracting.
The 3rd shot gives you some idea of how close focusing the Tamron lens is, too.... to around five feet! That's pretty amazing for a relatively inexpensive lens. (The nearly $10,000 Canon EF 500mm f/4L IS USM II's closest focusing distance is about 12 feet.)
The Tamron SP 500mm Model #55B "mirror" lens dates from 1979 and can typically be found used for between $100 and $200 (on everybody's favorite auction website). However, be careful. Originally that lens was fitted with a tripod mounting ring and came with lens hood and several small filters... One of which is a one-stop neutral density. I feel it's important to get a lens that still has the tripod mounting ring... Where it hasn't been removed and lost (or the later version that deleted the tripod ring). IMO, that mounting ring is needed to effectively use the lens on tripods and monopods, which will be necessary sometimes with a powerful telephoto like this... ESPECIALLY when using it on a modern, crop-sensor DSLR. If it's been lost, the tripod ring is virtually impossible to replace. The lens hood is also difficult (I think I bought the last replacement, matching hood still available new about 10 or 15 years ago... and it cost $40 back then, for the lens hood alone!). So, I'd recommend holding out for one that has both the tripod ring and lens hood, even if it costs a little more.
In 1983 Tamron updated the lens (from model #55B to model #55BB).... part of which included redesigning it without any tripod mounting ring and no longer including the set of filters. There were some optical changes too... Personally I still prefer the earlier version which has the tripod mounting ring.
If lost or not included, the filters are pretty easily replaceable. There should always be at least a clear "sky" filter installed on the rear element of the lens, a filter is part of the optical formula. The filters are 30.5mm, if memory serves... not a really common size, but not impossible to find either. With digital only the clear "sky" filter and one or two neutral density filters are needed maybe a half stop and a full stop or two-stop. Mirror lenses do not have an adjustable aperture (well, most of them don't... I know of two that do). The neutral density filters are used to reduce the light passing through the lens, if needed. A one stop filter makes it an effective f/16... and a two-stop would make it an effective f/22. (Note: because the aperture diameter doesn't actually doesn't change, depth of field remains the same regardless.)
The SP 500mm f/8 lenses are part of Tamron's Adaptall-2 line. That's an interchangeable mount that allows the lens to be set up to work on virtually any 35mm film or most modern DSLR systems. Adaptall-2 mounts are still being manufactured in China. I've bought them for EOS/EF mount cameras like yours for $40 ("chipped" version, which allows Focus Confirmation on Canon cameras to work). I'm currently using one on a Tamron SP 90mm Macro Adaptall-2 lens (also have Adaptall-2 mounts for Nikon F, Pentax P/K, Olympus OM, Canon FD and Konica K/AR, which allow all Adaptall-2 lenses to easily be converted to work with various vintage cameras in my collection.) There also were some excellent Adaptall-2 mount Tamron SP 180mm f/2.5, 80-200mm f/2.8, 300mm f/2.8 and 400mm f/4 manual focus lenses. There was an SP 350mm f/5.6 mirror lens, too... but it's a lot less common than the 500mm and because of its rarity tends to bring 2X the price or more.
You might see the Tamron 500mm offered with a "matched" 2X teleconverter. Sometimes they were sold that way. Frankly, I tried the lens with various teleconverters and never found a combo that gave what I considered acceptable image quality. As good as the lens is optically on it's own, IMO it just doesn't work well with teleconverters. (Note: Tamron's much bigger and more expensive 300mm f/2.8 and 400mm f/4 Adaptall-2 lenses both work very well with 1.4X teleconverters and pretty well with 2X... but good copies of those lenses cost a great deal more, even used. Beware, too, a lot of them were owned by newspapers and magazines, as part of their photo equipment pools, shared among staff photographers. Pool lenses are often very heavily used... and none too carefully treated by their users.)
I foolishly sold my Tamron SP 500mm f/8 some years ago, only because I had another similar telephoto for use on the camera system I was using at the time..... Sometimes I wish I'd kept that Tamron!