I can't stand Burnley and think they will go down. That being said they run a tightly budgeted ship and graft hard and dirty to grind results. Don't like it but admire it in a leage owned by many billionaires.
Palace like most have said, losing that many players and getting a manager in with no prem experience will be a tough ask.
Third spot is hard, as are all to be fair, could have gone Norwich, Newcastle, Brentford or even Wolves as all don't look very good at all but I've gone Watford. Norwich will improve I feel after no pre season, Newcastle got Wilson and ASM who will get goals, Brentford seem to have a buzz about them (sorry) and wolves just to survive if they can get jiminez firing, Trincao looks like he could be very good and Neto to come back. But fair few clubs be fighting down there I reckon.