One of those lens built in models (to avoid the ever-present dust) that zooms from 24 to 400mm (you need 400mm for the wildlife) would be ideal. The faster the lens, the better (and the more expensive). Dust sealed would also be great (but ziplocks work well, too).
Over on dpreview.com, use the Cameras > Camera feature search menu item and under Optics & Focus select 25mm, 320mm, F2.8 and there are 16 cameras to choose from. All but one are under $500 except for the highest rated, the Panasonic Lumix DMC-FZ200 (80%, but $600). The second-highest rating of 76% went to the Panasonic Lumix DMC-FZ150 at $499. This might, at least, help to narrow your search.