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the big problem I see for the OP is that there are lots of different approaches to this issue, all of which are a function of origonal budget.
I consider myself as a serious amature with respect to wildlife in general, and birds specifically, yet I have not ventured into the stratosphere (yet) and joined the 100mm+ club (lenses more than 100mm in diameter)
if you consider that you want something in the 400-500mm range, but still retaining good sharpness, I see realistically about 4 price thresholds, I have put them somewhat arbitrairly
<$250
manual focus 400mm F5.6 lenses such as SMC and Takumar or third party like Vivitar. There are also mirror lenses in this category.
Note that these lenses are not internal focus, and as a result donot close focus, and also suffer from CA.
Note all of these lenses are slow to focus, but accurate, due to the large rotation required to go from infinity to minimum focus.
$600-$800
In this range are many used zooms, like the first generation Sigma APO 70-200 F2.8 EX and you can add a TC for ~200. You can also find some SMC or Takumar 500mm F4.5 lenses, but see all the notes in the <$250 range they all apply. You would also find in this range any of the pentax 300mm F4 lenses (Super Tak up to A mount) combined with the SMC-F 1.7x AF TC
$800-$1200
Look for new BIGMA and other up to 500mm Zooms from sigma, plus used Tamron 300mm F2.8 lenses (to which you would add the SMC-F 1.7x AF TC. Depending upon what TCs are available, new 70-200F2.8 lenses would also be in this range when you add 1 or 2 teleconverters
>>$2000 all the new lenses with 112mm filters or larger (sigma 300F2.8, 500 F4.5) plus used pentax A, F, FA mount super teles.
You need to decide how much the extra speed for the last category is worth, in terms of weight and hand holding