I like your advice of answering those three questions:

What’s your key message?
Why are you creating this design?
How do you want your users to feel?

before you start browsing colors. Sometimes I start browsing and don’t have a clear purpose in mind for the project and it takes me down wormholes that I probably don’t have to go down. Clarifying and bringing to the surface the message and purpose you have can do wonders for selecting colors faster and more confidently.