Just one clarification to what Loonbeam said, as some folks get a little confused when people mention 'native' lenses or comment that the Sony APS-C mirrorless bodies don't have very many lenses compared to other mirrorless lines, etc. What most people are referring to are 'native APS-C lenses' - of which Sony has 16 APS-C specific e-mount lenses, plus another 8 third-party e-mount autofocus lenses. However, the 'FE' or full-frame e-mount lenses are still NATIVE e-mount lenses on APS-C bodies...no adapters, no loss of function or speed, etc. The only difference is that they can also mount on full-frame sensors without vignetting. Including FE lenses, Sony has 39 native e-mount lenses, and third party adds another 15 autofocus native lenses, for a total of 54 - which includes 32 primes and 22 zooms.
When it comes to the longer lenses, full-frame vs APS-C has very little impact on lens size and weight. Consider the Fuji 100-400mm lens which is designed for APS-C only, at 3.03 lbs and 3.73" x 8.29",
and the Sony 100-400mm lens designed for full frame at 3.07 lbs and 3.70" x 8.07". Nor does full frame have to mean 'huge' for all lenses either - the Sony 85mm F1.8 lens is a full framer weighing only 13oz measuring 3" x 3.2"...not exactly a monster. Some other FE primes are also reasonably small and light too.
Just wanted to clarify that one point as it can get a little confusing, with some folks thinking FE is a completely different mount...and a common criticism of Sony's e-mount is that they have fewer lenses than other mirrorless, because only their APS-C lenses are being considered.
My uncle who is a serious bird and nature photographer wrote to me saying he has a A6000 and he pairs it with high-quality Canon glass via a converter. This is interesting--I didn't realize you could do that. I wonder if I could still use my Tamron 16-300 when needed.
I too am heavily into bird and wildlife photography, and use both DSLRs and mirrorless bodies for it - my A6300 is my favorite camera for birds-in-flight photography as the autofocus and tracking is superb and the camera is extremely fast and easy to handle. My main lens for this camera is the FE70-300mm, which is a wonderful lens - and I'm also looking to add the FE100-400mm lens coming next month. If you do decide to use other lenses from other mounts via adapters, you may want to look at the A6300 or A6500, instead of the A6000 as they upgraded the focus system to work much better with adapted lenses...the difference is very noticeable. I use an Alpha-mount Tamron 150-600mm lens on my A6300 to great effect - it was almost unusably slow when I used it on my A6000.