Depending on the type of music I'm making, I'll employ various tools. For WeeklyBeats (and other electronic oriented productions), my usual/preferred starting point is the Matrix device in Reason since you can take a simple idea/pattern and mold it like clay. From there, I'll use that content to generate the other instrument layers and create a framework for the piece. If things are pleasing to my ear, I'll start getting inspiration for other elements, like melody, bass, form, and/or narrative.     

Compositional process inspiration comes from the pattern use and manipulation in the music of Ligeti, Reich, Riley, Lang, and Gordon. Vibe and Atmosphere inspiration comes from artists like Prefuse 73, Boards of Canada, Amon Tobin, Air, Trent Reznor, and Battles. These all slip into my mind in various ways.   

From there, it becomes a stew in my mind that I'm still trying to figure out.