What are the essential lenses for bird photography? Somewhat of a difficult question, in part due to the fact that even bird photography can vary quite a bit. But lets assume that the birds are not that close and for the most part are either quite small or rather far away.
This means that you are going to want a crop sensor camera which will provide the benefit of the apparent crop factor on the focal length which is 1.5 times larger with Nikon an Sony or 1.6 times with Canon. This effectively turns a 100mm lens into a 150mm or a 200mm into a 300mm lens! (okay I used the Nikon and Sony factor simply because it is easier)
There are two vital lenses in a photographers bag, the 70-200mm 2.8 which is a lens that has been around for a long time and pretty much has been perfected. Short enough to capture those close photos and long enough to get the smaller birds. The wide aperture allows some nice bokeh on close ground birds and permits shooting in the lower light. Pairing this with a teleconverter is also possible, giving an increased zoom range of roughly 100mm to 280mm if a 1.4 teleconverter is used. (and an effective length of 150mm to 420mm on a crop sensor camera. The second lens is something in the 200-500mm f/5.6 range. There are longer range lenses in the 150mm-600mm length, which can be more convenient but are generally not quite as sharp in focus but can also be used if that is what you want. My pick being the 200-500mm as it pairs very nicely with the 70-200mm lens. Both the 70-200mm 2.8 and 200-500mm 5.6 are able to focus quite closely (typically in the five foot range for the former and up to perhaps the 8 foot range for the later – still quite close for the focal length).
The lenses you pick should also be able to focus quite quickly for birds in flight, although the 70-200mm will always be the fastest in focus, they both should be quite good.
Once you have these two lenses – get out and shoot photos! There is little you can not capture and do well.
The next think you need, which is not really the lens itself, is a camera body with a suburb focusing system and fast shooting speed. There is not much more demanding than bird photography for those two aspects of a camera. In this area Sony and Nikon pretty much hold the top with the Sony A7 or Nikon D500 (or D850). (the D850 is not a crop camera but resolution is high enough that even cropped it can match any crop camera)
Do you need a tripod and gimbal? Yes, a good idea. However, if you get good quality lenses in above lengths, some of vibration reductions systems today can allow you to almost forgo those in many cases. The Nikon 200-500mm 5.6 as an example is claimed to have a VR reduction of 4.5 stops – and in testing it is pretty much able to meet that claim! That means shooting at speeds of 1/50th of a second when at 500mm is quite possible with excellent results! ( I don’t do that but have tested it and obtained amazing results )
Get a camera – lenses – get out and enjoy.