Starglider is a 3D space shooter created by the young programmer Jez San and published by Rainbird in 1986. It was released for the Commodore 64, Atari ST, Apple II, ZX Spectrum, and other computers. The Amiga version was released in 1987.
Jeremy San initially created the game for 16-bit computers, most probably Atari ST, but despite this, he opted for wireframe vector graphics, like his favorite arcade, Star Wars. The sequel, Starglider II, would be much more advanced regarding gfx.
Starglider was a huge success, especially in the UK, where it was also featured in TV shows. The sales made Argonaut Software, the company founded by Jez San, very popular. Thanks to this, Nintendo decided to create a chip called Super FX to provide 3D graphics on its consoles. Argonaut developed the game Star Fox to use this chip.
Back to Starglider, despite the simple visuals, it was pretty advanced for its time. The gameplay was fast and addictive. The Amiga version included a soundtrack composed by David Lowe, using one of the earliest examples of digitized instruments sounds. The game package also included a sci-fi novella written by James Follett (brother of the more famous Ken), describing the backstory.
Starglider was voted #2 Best Amiga game in 1987, and it won another prize for Best Digitized Speech (the voice was Clare Edgeley, a Rainbird employee).
If you want a real 3D space shooting experience from the '80s, you can't choose a game better than this.