If you're starting from scratch, the main goal is a contrast ratio that suits the needs of the font size and weight. Larger and bolder fonts need a much lower contrast ratio. This is very important for logos and any image that includes text, as the browser zoom tool won't necessarily enlarge images enough to make the text more distinct.
Also, you're better off making the contrast higher than the minimum ratios. I'll typically start with the colors I want to use in the design, implement and then test the colors with a tool like the color contrast analyzer Chrome extension. I'll then make small changes to get a good contrast and still the colors I want to use. Webaim.org has a lot of information and good analysis tool. Also, I recommend reading the W3C recommendations.