I've only really done a couple of remixes, since I mainly focus on originals and stuff. As such, my remixes are more "DystoP remake" than "song transformed into another genre" or something.
Useful things to have from the song you're remixing are the key, BPM, and stems. Even just having the off vocal and acapella can be an excellent reference point. The most important elements to keep would be the chord progression and main melody, although that isn't necessary, since some remixes are just breaking a song into samples and then rearranging them into another song entirely... But basically, I think the easiest type of remix to do is to try remaking the song?
Also, there's all the resources and stuff that people post around here for writing originals. You should definitely check those out.