Hi Lars,
I'm primarily a birder, and either have or have owned most of the ~500mm alternatives except for any of the Sigma xx(x)-500 zooms as IMO, I have found better alternatives for the way I like to shoot.
My most used is the FA* 300 f4.5 + the P F 1.7x Auto Focusing Adapter for handheld shots. At f7.7 wide open, it sounds slow, but it's fast enough for most daylight conditions, and the AF only struggles in pretty dark overcast or deep shadows. The fact that the lens is very sharp wide open helps because I don't have to stop down to get good results. Compared to the Sigma >>500 zooms, it's within about 1/2 stop at max aperture, but taking handling into account, it's a much better alternative, IMO. Any 300mm ~f4 is going to weigh @ 1 kg (2 lbs and change), and the 1.7x AFA only adds a few oz, but the Sigmas weigh @ 1.6 kg (3.6 lbs) and at 500mm, the lenses have to extend to about double their shortest length, so the heavy front element is hanging way out there, so the balance point moves forward significantly. This is a concern for two reasons: It adds a degree of difficulty to handholding, and the shifting balance point can make the lens more difficult to use when mounted on a tripod, especially with a gimbal.
I actually have four 300mms with max apertures @ f4: The mentioned FA* 300/4.5, a Canon FD 300/4 L converted to K mount, a Sigma EX 100-300/4, and an MF Tokina 100-300/4 AT-X SD. The FA* and Canon L are very close in IQ and size/weight, but the FA* usually gets the nod when I'm going to pair it with the 1.7x AFA because it's much faster to manually prefocus with about 180° of focus ring rotation compared to @ 270° for the Canon. The FA* also focuses closer with the MFD at 2m vs the Canon at @ 3m (@ 6ft vs @ 10 ft), which is important to me because I often can shoot very close. The Sigma, though close to the same level of IQ, is slightly softer with the AFA, and weighs about a lb more, so unless I feel I'd want the zoom, it tends to stay home. I was a bit disappointed with the IQ of the Tokina. Reviews that I've read suggest that this lens is also close to prime sharp, but my copy isn't in the same class as the other three.
There are less expensive 300mm f4 alternatives. There are the Pentax K 300/4, M*300/4, and A* 300/4. All of them are very good with the 1.7x AFA. The K is significantly larger and heavier than the later models as the M* and A* are the smallest 300/4s ever made, IIRC. All of these lenses are less desirable for me for two main reasons: All have MFDs at 4m (@13 ft), and none use ED glass to control CA/PF. They all are sharp wide open, and are convenient in size and weight. CA/PF is reasonably easy to correct in PP, so that should not be much of a problem, but for me, the MFD is the deal breaker as I often get ops to shoot at much shorter distances, but I've been doing this for quite a while, so I probably get more of these short range opportunities than many because of this experience. Prices for these seem to be reasonably stable at @ $300-400 for the K, $400-500 for the M*, and $500-600 for the A*. Of these, the A* is the most desirable because of the automatic diaphragm. With the 1.7x AFA, the max aperture becomes f6.8, and that's really close to the AF systems limit (@ f8). This makes it fiddly to use a full manual lens if you want to stop down and still use the AF advantage of the AFA.
I also have one of the Tokina 150-500 f5/6 SDs. It's a very nice lens (especially for the price I bought it at), but at f5.6, it will only work with the AFA in the brightest conditions, and it's easily the biggest lens I own, so I'm unlikely to opt to carry it around much -- definitely a tripod only proposition for me. Another very inexpensive alternative is a 500mm f8 mirror lens. I have a Tamron SP 500/8 Cat in Adaptall 2, and it's a very lightweight alternative, but it's difficult to handhold because it is so light, and the DOF is very thin, so MF is tricky. IQ is very good, and then there's the infamous donut bokeh to contend with.
Then there are the 300mm f2.8s. Probably the only one that is within budget would be the Tamron SP 300/2.8 LD IF Adaptall 2. There are 3 models, with the 60B the most easily available, but the 360B is good if you can find one at a good price. With the AFA , this becomes a 510mm f4.8, so the specs rival the $4K Sigma EX 500 f4.5, and except for some lack of CA/PF control, this combo is close to as sharp at 1/4 of the cost. You do need to consider that you'll want a PK/A adapter, so have to add the cost of one of these to the equation, but 60Bs with a lot of cosmetic damage, but good optics and mechanics can be found for as little as $300-400. I've found this combo to be handholdable in the past, but as my body ages, this becomes less practical for me. . .I'm 63 YO and 5'5" with some significant physical limitations, so YMMV.
Here are a few examples with 300mm + AFA combos with different lenses and bodies:
K-5 IIs with the FA* 300/4.5 + AFA lens wide open, 1/250, ISO 140 This was handheld and just downsized for posting
K-5 IIs with the FA* 300/4.5 + AFA lens wide open, 1/250, ISO 4500 This was handheld and with NR and sharpening applied in PP, then downsized for posting
K-5 with the Canon FD 300/4 L + AFA, lens wide open 1/320, ISO 1600. Shot off a tripod with NR and sharpening applied, cropped on the left side to 8x10 and downsized for posting
K-5 IIs with the FA* 300/4.5 + AFA lens wide open 1/1250, ISO 800 This was handheld and with NR and sharpening applied, cropped on the right side to 8x10 and downsized for posting
K100D with the FA* 300/4.5 + AFA lens wide open 1/400, ISO 200 This was handheld and cropped from the top and bottom to 8x10 and downsized for posting
K10D with the FA* 300/4.5 + AFA lens at f 6.1, ISO 320 This was handheld with NR and sharpening applied and cropped to 5x7 and downsized for posting
This one's with the DS with the Tamron SP 300/2.8 + AFA + Tamron SP 140F Adaptall 2 1.4x TC (this is an advantage that the faster lens allows -- you can stack a TC with the AFA and retain AF with the max aperture at f6.7) This was handheld (with no SR available BTW) 1/250, ISO 400 slight sharpening and CA/PF correction applied, cropped from the right side to 8x10 and downsized for posting.
This is a 100% crop from just below and left of the center of the frame. There has been no PP applied. This shows how, with a very good lens, good TCs don't degrade IQ anywhere nearly as badly as some seem to always suggest.
Good luck in your search!
Scott