I don't know that this is the case but even though the sink may be
attached to the wall, the vanity may be supporting it. From the photo,
that sink looks heavy. And I think removing the sink first would make
it easier to remove the vanity.

Just some random thoughts while someone else comes by with more...

Obviously planning is key. Having all the stuff you need ahead of time
will cut down the time that the room is unuseable.

You could do some of the demolition yourself, in the evenings, while
keeping the bathroom useable... pulling up the flooring, for example,
and cleaning up the subfloor [if necessary] to get ready for the new
floor.
A note - If you build up the flooring too much the drainpipe your
toilet connects to will be too short.
You could pull out the vanity and brace the sink [if necessary].

I'm a little unclear on the ceramic tile. Are you going to rip it all
out, or do you want to fill in the notch that'll be left after the sink
is out [or do you want to bring the tile down, if necessary, to meet up
with the new sink]? If you're going to rip it all out, do whatever is
quick [without damaging any wiring or water lines].

Put off whatever you can, like the door moulding. You can do that
later. The moulding looks like regular stock stuff, from what I can
tell in the photo.

If you haven't done drywall before then it probably is best left to a
contractor. They're pretty quick, and getting that smooth flat surface
can be a bear for a first-timer.