I do a mixture of approaches; I do chain piecing when I'm working on a project with lots of the same kind of piecing and I also alternate from cutting to piecing to pressing, not necessarily in that order. I think of the song from Music Man, 'Pick-a-Little' because it's how I think of my approach to sewing; cut-a-little, piece-a-little, press-a-little, piece, piece, piece - - -
Although I must qualify that by saying when I'm first starting on a project, I'll make up one block completely to 'audition' the fabrics and be sure I like how everything looks and adjust as needed.