That web site will help you identify the weeds you're targeting, and PBI Gordon's recommended product.
You've learned the difference between broadleaf and grassy weeds. Keep searching here for more and more and even more specific details!
That being said, Image is a very good product with a broad range of control of grassy and broadleaf weeds. But it will discolor bermuda, and can really stunt it bad if the turf is not healthy.
Now go slowly, grasshopper! The trick is to not total a lawn while you're killing the weeds!
One of the best tips I learned early on from this forum was to add a little liquid N or liquid Iron to your spray mix. It helps the target uptake the chemical and helps the grass recover from the injury.