My brother is looking for a mirrorless camera kit for wildlife for around $3,000. Could go as high as $4,000 if absolutely necessary. He knows there will be limitations with his budget. It has to be capable of taking action photos.
Depends on how much wildlife experience your brother has...
For a begginer, at under 3000$ a used Nikon D500 and a 200-500F5.6/300mm f4 PF/ used 500mm PF are, IMHO, still the best option.
While newer mirrorless cameras might have more bells and whistles, as a reliable, usable in the filed system, the old Nikon D500 still stands with the best of them (e.g: it gave the A9 and 100-400 a run for it's money when shooting seagulls in a feeding freenzy... and that's with a sluggish Sigma 150-600mm C).
If it must be a mirroless camera, he should stretch the budget to 4k and go for the OM-1 and a used 300mm f4 (and assorted TC's). If I were starting fresh, I'd pick this set-up for wildlife (especially birds) over any 20-ish Mpx camera(even FF) and a 200-600-ish zoom. Just add a pinch of DXOs PureRAW and between that, the nearly 2 stops faster and very sharp lens, the speed of the camera and the miriad of functions, you are more likely than not to get the sharper, better looking photo over even FF alternates.
I'd avoid the 100-400 zoom's though... not really that great.
But the most important thing:
Most people vastly overbuy their gear. If you look at the presentation section of this site, of all the wildlife shots posted in the past week, there might be 3 or 5* that couldn't have been taken with a D7200 and the old AF-S 300mm f4D lens using the old noggin'. And that combo can be had for under 1000$ if you dig a bit through the used market...
*except maybe the true macro ones that do need a 1:1 lens
