The inventor of the Amiga 1000 was Jay Miner, who created the Atari 800 many years before. He wanted to make the most powerful computer ever, then he joined a small Californian company called Amiga. He used the principle of the three coprocessors (again) to help the main processor. At the beginning, the Amiga had only 64 kilobytes of RAM! The original "Amiga" called the Lorraine was meant to be a game machine with some computer capabilities.
Atari initially invested the money in the Amiga Corp. to do the R&D on the Amiga computer line. Naturally, when the design was finished, Amiga Corp. gave Atari the choice to purchase the technology. Atari passed in favor of their own project. Amiga Corp. then offered the technology to Commodore, Inc., who were quite pleased to purchase it, seeing that their own 16-bit computer was so far from reaching the shelf.
After the loss of a major legal battle for control of the Amiga chip set design, Atari launched the ST series (Sixteen-Thirty-two) as a competitor for the upcoming Amiga.
The operating system (AmigaDOS) was done by MetaComCo, a British company who specialized in the 68000 processor (they also made languages for the Sinclair QL). It is a fully multitasking system which looks like UNIX with a graphical user interface.
It was the very first personal computer with great graphics and sound capabilities with a GUI environment.
The Amiga BASIC was written by Microsoft (like most other versions of BASIC), but the first models were shipped with a non-Microsoft BASIC called ABasiC.
The Amiga 1000 was to lose popularity one year later with the creation of its two main successors: the Amiga 500 and the Amiga 2000.
There were two versions of the Amiga 1000. The first one sold only in the USA, had a NTSC display and no EHB video mode. Later versions would have this built in. The second one had a PAL display, the enhanced video modes (EHB) and was built in Germany.
The official name for the A1000 was the Commodore Amiga. It was only when the A2000 was launched that they officially began to refer to the machine by its model number.