A bridge camera. I have travelled with several throughout the years and for your purposes I don't think you can go wrong. I have been partial to Panasonic the past few years, the FZ200 or 300 are good cameras that could be had for under $300. They are a few years old but you don't need anything super fancy...though they have all the fancy settings too. Best feature about them is they are F2.8 through the whole zoom range which is large at 25-600mm. It would be a light easy to carry camera that gives you lots of flexibility no matter where the animals are. Panasonic has newer FZ1000 and 2000 models with better video. Canon, Olympus, Nikon et al have bridge cameras too.
I used my FZ200 for our Antarctic trip and came away very happy with what I ended up with. Comparing shots to what the pro on the trip took I'd say my scenery shots were very similar, with good light my animal pics were quite good, and in fast action I lost out as the lens wasn't fast enough...but trying to get a porpoising penguin is tough and even the pro on the trip with a $16k 600mm Nikon lens trashed a ton of images. The ones he did keep were amazing though.
A couple of my pics:
In general I think my shots are fine. They aren't pro level, but I'm not a pro, don't expect to be one, and don't want to carry 50 lbs of camera gear.
I do have an older Panasonic FZ150, with the same 25-600 lens but isn't F2.8 through the entire range which I would sell for a low price. I have extra batteries for it too.