Attach wallpaper to all walls, and ceiling (open to suggestion if it could look better with one or more walls without the same wallpaper)
Attach a new toilet
Attach new sink/drawers/lights
Does that seem like a reasonable order of steps for a DIY bath remodel? Also, should I use the same pattern for all walls and ceilings? This is my first home and don’t really have an eye for this stuff.
I'd remove the toilet first and re-install it last -- the vanity (industry term for the cabinet below a bathroom sink) will be easier to manage with the toilet out of the way.
Things to beware of:
the existing flooring may have been trimmed around the vanity. If the footprint of the new vanity does not match or exceed the existing one you'll have to figure out how to cover the difference. A small difference can be covered with baseboard, 1/4 round shoe molding, or a combination of the two but if the difference is significant you may be looking at installing new flooring too.
it happens all too often that people are lazy and don't paint or finish the wall well behind the toilet tank. You may have to deal with drips/runs/lumps in the wall paint if the new tank will be a different shape/size to the old one.
same potential for rough edges around/behind the mirror, vanity, and light bar. Surface irregularities are likely to show through wallpaper, so take the time to smooth any that you might discover.
confirm in advance that the shutoff valves for the toilet and sink water supplies work.
check the position of the sink supply and drain plumbing and consider how it'll work with the new vanity and sink position. It may be necessary to modify the vanity; in extreme cases a particular vanity just can't be made to work with the plumbing as-is.