A satisfying vertically scrolling space shooter? On MY 1980s computer? It's more likely than you think!
Silpheed was one of the fruits of the deal that Sierra struck with the Japanese company Game Arts (who would go on to create Lunar, Grandia and some other noteworthy stuff) to port and localize some of their early MSX and PC-8801 games. It's arguably the best of the bunch that got ported (only Zeliard challenges it.) Though the Sierra port for MS-DOS came out in 1988, the game was originally released in 1986 in Japan and is noteworthy for technical wonkery like using wireframe polygonal ship models with an isometric perspective, having rotating wireframes of every ship in the game with Gundam-like statistical breakdowns if you let the title screen run for a bit, etc.
Settle down, Robocop
Even if you're not one to wonk out with your conch out, you can still appreciate the very solid gameplay and design as well as the good soundtrack. It manages to be challenging while feeling fair the whole way, without having to resort to masochist gimmickrey like memorization of entire levels or "bullet hell" shenanigans. There's no lives - if you die you go back to the beginning, but your shields allow you to absorb quite a few hits. You can partially restore them by picking up power-ups in the levels and they get fully recharged between levels as well. Weapons and power-ups stack, so you don't have to worry about accidentally picking up some crap you didn't want. And in between levels you gradually get a choice of upgraded starting guns, which I believe depends on your total amount of points.
Though it never really feels cheap, Silpheed is pretty tough ... but the "restart from the beginning" thing ceases to become a problem when you discover the semi-hidden feature that allows you to continue at the last level by pressing F10 after starting a new game. I dunno why they hid this on a function key instead of putting it in plain sight; it's the one (very) minor slight against the game, but whatevs. Oh, and the only other minor knock is that they have like two boss types that they keep recycling, they just keep getting new weapons each time you see them. It's wireframe graphics in 1986 though, I think we can give them a pass here.
Classic PC shooter badassery right here. Both the levels and the soundtrack keep getting more interesting as you go on. Highly recommended.