My suggestion is that if you can, purchase any Nikkor lens with ED glass. The ED glass Nikkors all have no stopped infinity focus point, they in fact focus past infinity.
This may not sound important, but in extreme heat the expansion factor may make it impossible to focus dead accurately.
If you can, get a lens with IF-ED, which is Internal Focusing with ED glass. ED is Nikon talk for an apochromatic corrected bit of glass. The colours you obtain with ED glass really are at the top of the tree especially with regards to colour fringing, they just don't do it.
Colour fringing is where one colour starts to bleed or merge with another or others, something you will find is reasonably common in the lower range of lenses by aftermarket manufacturers in the lenses that were being manufactured at the same time as your F3 was manufactured. Lenses manufactured more recently should be better, I don't know for sure though.
Possibly the best lens that is a budget lens, although that is of course subjective and dependent upon the size of you pocket, is the f/5.6 600. This is a very good lens for bird photography, but it really needs a tripod and that tripod should be equipped with a fluid head. In my years of fiddling around with lenses and tripods, this combination was the very best I have ever used.
One other addition, equip your F3 with the MD4 drive, if you don't have one. If you wish to photograph fast moving objects and in quick succession sometimes, then a drive is brilliant.
Another possible addition in your aid to records, is to add the MF18 data back. This is the best data back Nikon made for manual cameras. Data is recorded vertically in-between the frames, you can have a sequential numbering set-up or the date, your choice. I myself use the sequential numbering set-up, makes knowing in which sequence any roll of film has been shot easy to figure out. You will be told that the MF18 Data back can only be used with the MD4 attached, not quite correct. The reason this is stipulated is because there is a bottom prong which sits below the camera and sits over the outside contacts of the MD4. You can safely operate the camera with the MF18 data back without an MD4 attached, just take care with the protuberance.
The f/2 300 surely has more than 40 odd units out there, I have seen two myself and used one for a ½ a day whilst my 600 was used by the photographer who owned the 300. One thing I can tell you, is that the f/2 300 and the f/5.6 600 weigh about the same. The cost of the f/2 300 at the time of the purchase for that photographer, was literally ½ the price for a standard house in Melbourne, it was a lot of money in anyone's language.
The cheapest good glass for your purposes may be the f/5.6 400 Nikkor, it uses 72mm filter size, which is a Nikon standard for many of their lenses. This lens can be used hand held wide open with, but you really need the F3 equipped with the MD4 drive so your right hand can really take a fair whack of the weight, otherwise you will find yourself shaking after only a short period of time. The 400 is not a sought after lens as it isn't considered fast and it's length is considered too short compared to the longer lenses.
Regarding accuracy of apertures and/or stops, when shooting transparencies for critical work in the past, 1/10 of a stop aperture settings was what we used on both Mamiya and Hasselblad lenses. These were calibrated and marked lenses with a sheet telling you at what actual position to put the aperture ring, to obtain a very accurate f stop.
Regarding the ultimate set-up in Nikon land for bird photography. A person I knew spent the wet season in the top end of Australia with a Nikkor f/5.6 800 and a very good tripod, these were possibly the very best bird pictures I have ever seen. One of these came up for sale recently, it was offered to me for around $10,000 AUD it would have been brilliant, but I couldn't justify spending that amount of money.
As a matter of interest, the 400 f/5.6 is a brilliant lens for portraits with a difference, but a very helpful addition is a two way radio system, with the talk button at the photographer's end taped down and the radio at the other end within earshot of the sitter. This facilitates position changes without shouting, yelling out loud means you have to take your concentration away from the viewfinder, not conducive to great portrait taking.
Mick.