The picture is not totally clear, it sounds like you want to tear out
enough below-counter cabinetry to put in a dishwasher, replace your
sink, and replace the tile backsplash. Barring complications, I'd
replace the tile first cause that will make a mess. Then the sink so
that the plumbing can be updated to allow for the dishwasher, then the
dishawasher last. Better yet would be to do the sink and dishwasher at
the same time, that's one trade, the plumber, that can do all that.
Note that for a dishwasher you probably need a separate circuit, not
sure if that's a 'code' item or if it's just a good odea because the
thing pulls so much electricity.
Usually/often the dishwasher connects into the garbage disposal. If
you don't have one and want to add one, that's another circuit 'I