Wildlife is going to be pretty lens heavy. You'll want at least 400mm equivalent.

As r/photography likes to say, the equipment is really personal to you. For example, I absolutely hate using Canon cameras, something about their UI just puts me off; I'm a good deal slower when using them. If possible you should try out some cameras to see what sticks. If you're serious I'd suggest renting something that catches your eye and is around your budget to try.

If you're on a budget a DSLR is actually a great pick; you probably can get a higher level body used with some really cheap 80-400/100-400/150-600mm type lenses now. Saw on my local Amazon a Tamron 150-600mm G1 new being cleared for like under US1k.

Edit: Also, stating your budget will really get you more targeted recommendations.