By the time of Voyager, we were reasonably familiar with most of the players in the Alpha and Beta quadrants of the galaxy. We knew that the Borg were our main adversary from the Delta Quadrant and that the Dominion were in the Gamma Quadrant, but there was fairly little known about the Gamma and Delta Quadrants still. My question is out of universe, why did the Production team decide to set Star Trek: Voyager in the Delta Quadrant rather than the Gamma Quadrant, or another galaxy altogether?
According to the Memory Alpha article on the Delta Quadrant, the decision (to set the series in the Delta Quadrant) was made based on a suggestion by Michael Okuda to Rick Berman in 1993:
The Delta Quadrant was originally suggested as the setting for Star Trek: Voyager by Michael Okuda. On 27 September 1993, he sent a memo to Rick Berman that stated, "Since the Gamma Quadrant is the province of ships from DS9, suggest that this new show be set in the Delta Quadrant. One of the few things we know about the Delta Quadrant is that the Borg homeworld is located somewhere there. This might present opportunities for the Borg to be recurring bad guys." (A Vision of the Future - Star Trek: Voyager, pp. 207-208)