As for the dungeon of their choice, it would have to be the same one that they entered beforehand. It was simply the best choice considering their opportunities. When one clears a dungeon that wasn't explored previously, they can receive drops from slain monsters and also find treasure chests.
However, those dungeons were not open to the public. All dungeons were owned by the United States and its governing body, who would lease the dungeons to contracted guilds.
The only way Kaiden and co could enter a 'virgin' dungeon was to either create their own guild and pay millions, if not billions of dollars for each dungeon contract, or to swear allegiance to a guild that owned such dungeons.
The former option was simply not feasible for the time being, while the latter was not something Kaiden wanted to do.
Guilds were strict organizations, he wanted to be his own man. Kaiden cherished freedom and independence greatly.
