I've posted pics from numerous vintage lenses in the 300mm plus lens club - discuss your long lenses thread.
Between 300mm and 400mm I would suggest if you're looking for reach then 400mm (500mm options are really limited outside of mirrors). But the usually closer focussing of the 300's might sway that.
I would suggest that the no 1 vintage lens to go for is the sigma apo 400mm f5.6 in PKA mount but unfortunately that is chronically afflicted with a hazed inner doublet - cement deterioration. It is possible to find one with only slight haze. Note this is distinct from the sigma (NON apo ) MC 400mm f5.6 this is very similar structurally - compact with internal focusing. This has the cachet of being available with KAF autofocus mount. I have one and have been trying to use and like it without success so far - it is difficult to get to nail focus and is a CA fringing monster.
I wrote the
review on the nestar IMO it is the best of the original t-mount lenses from the 1960's/70's. However the later tokina made 400mm f6.3's are just about as good, focus closer and already have a tripod mount and hood, these are diy add ons for the nestar. The tokina is found in own name, soligor, optomax incarnations. Then there are the vivitar 400mm f5.6's. The tokina made ones come in two versions, a lerger heavir one with tripod mount and a later one that is essentially a rebadged tokina RMC. These are all similar performers. The premium tokina 400mm f5.6 is the last version the
SD 400mm f5.6 which can be found in PKA mount. I managed to find one in your price range but that was a one-off. In practice it is only a bit better than the others IMO.
I had a dud tamron 500mm mirror too - I tried hard to make it work/check it out but no luck. But that was an exception, I have had a dozen + of these pass through my hands and still have a couple, and what I note is the consistent quality. Check out pics in the mirror lens club thread.
Finally, I have seen the early model 55-300mm DAL's sell within your price range recently.