Claw Marks provides details on all of the ribbons but unfortunately the pages that describe them are in black and white. The best way to see the order of precedence would be to look at a screenshot from WC1 of a player's awards after they have received all of them:
After that, you need to reference Claw Marks to see which ribbon is which. Doing that, we see that the order of precedence is, from left to right:
Top Row: Academy Graduation, Flight Training, Vega Sector Campaign, Ace Ribbon (5 Kills)
Middle Row: Ace of Aces (25 Kills), Five Missions, Ten Missions, Fifteen Missions
Bottom Row: Hornet Qualification, Scimitar Qualification, Raptor Qualification, Rapier Qualification
On most military uniforms, medals are represented by ribbons that match the ribbon pattern of the medal which are worn with other award ribbons, but in the Terran Confederation Navy of this time period (2654), the medals are worn separately on the uniform. A bar matching the ribbon color is added for each subsequent award. For example, the pilot depicted has received the Bronze Star seven times. From left to right:
Bronze Star, Silver Star, Gold Star, Blank (This is where the Golden Sun Ejection Survival medal would go), TC Medal of Valor.
Hope this answers your questions!