I've always been fond of the way Ikaruga segments its stages and music together, even though the synth orchestra texture doesn't do much for me on its own.
I suppose it somewhat fits into the mentioned rock song structure, where the first movement is a soaring prelude that plays over the opening waves as the ship flies into the combat zone, then transitions into a more location-appropriate piece in sync with the haiku booster charge, marking the beginning of the stage proper. Altogether, very cohesive and experience-enhancing.
Genre-wise, my preference lies somewhere between
screaming Tecnosoft guitar and the driving electronic tracks of latter-day Dodonpachi like
Niji. Electronica is a terrifyingly wide net, so I'll not try to guess the subgenre on that one
Though really, I think the most important thing is that a given genre is able to host qualities that resonate with what's happening onscreen. It gets into vague artsy emotional experience territory, but things like the feelings of speed and flight are an easy pull for shmups - anything that can double down on the work's visual and mechanical themes, thus further pushing players into the flow state.
Despite being a remix, this
sweet 80s synth version of the Kyukyoku Tiger theme is a good example; listening to it, little imaginative work is needed for it to conjure up visions of a cool attack copter taking off and flying into battle. It probably owes a large part of that to the cultural echoes of Airwolf and the accompanying 80s synth that ended up resurging as vaporwave, but point being that it hits the thematic nail squarely on the head.
And, maligned as it may be, Touhou has some interesting stuff in that sense too - certain tracks like
Reach for the Moon and the terminally-memed
U.N. Owen pair the ebb and flow of the onscreen bullet hell with a chaotic push-pull composition that serves to further intensify the moment. Powerful stuff if employed correctly.