After new flooring, do I do skirting boards then paint; or paint then skirting+more paint?

Hi all,
I have just done laminate and wooden flooring in the downstairs of my flat in 3 rooms.

I had pulled up the old skirting boards so they need to be replaced, and I need to do a full paint job to all the walls as its 8 years old.
FYI, Walls and skirting will be a slightly different paint

Which should I do first:
Painting walls, then install skirting boards (then calking and then a touch up of repaint at the edges and paint skirting)?

or

Place skirting in, do the caulking, then do the painting of walls and skirting?

I'm sure there must be a preferred order for ease? (that I would only realise after halfway in).

Thanks in advance

We paint the skirting board to a finish coat and then fit it. Caulk the top, paint the walls and then paint the top of the skirting. Saves hours.

Good advice.. thanks..
Anything to make the arduous chore of painting half a flat a tad easier is always welcomed