I think the
Tamron Adaptall 300 f2.8
versions (and the related
400 f4) are a "GOOD" budget telephoto. They are manual focus, which will justifiably be a dealbreaker for some. Also the
Adaptall mounts are fiddly at best. Also too, like any long fast lens, they are very very big and heavy.
But otherwise you truly are getting a very high quality optical performer for fairly little cash.
Purple fringing is kind of medium, and everything else IQ wise is very good or great. Just a hair below the camera manufacturer's top of the line comparable lenses of the film era, which also still hold up today.
They take very well to many teleconverters. That will get you as far as 600 f5.6, which is respectable even on full frame for small birds. You will want even more reach, but that's always true.
The f2.8 means the image is very bright in the viewfinder and on the AF sensors for focus confirmation (less so when using teleconverters, of course).
Manual focus is a challenge. I do think a split prism viewfinder screen is highly beneficial, almost necessary, for focusing these guys. Unless you can use liveview all the time, which I cannot.
Everyone who goes to buy a supertelephoto seems to find out it is something like 3-4x their budget they set for themselves, and I guess it holds true even on the budget end. I've personally seen those lenses go on ebay for under $400, and you may, or (more likely) may not, get the right (and fully functional) adaptall mount or useful teleconverters at that kind of price, therefore possibly another purchase.
So not quite a kidney, but 3-4x what you were ready to spend.
Then expect to find out you probably must spend just as much all over again on tripod gear.