Hey everyone,
I have two things I want to say about all the other comments you've gotten, but first, I would like to point you to a blog post I have written for Holistic Songwriting which covers exactly what you're asking for:
9 Great Ways To Start A Song – Holistic Songwriting (Official Blog)
But anyways, here's 2 things I read in the comments that I disagree with:
1) There is no music or lyrics first. This is a common misconception in songwriting. You're not writing music and a poem and then combine them. In my experience, music doesn't work like that. It's a hybrid process where one thing leads to another. I might start with a melody, add lyrics to that and those lyrics take me to a line in the verse, under with I put the music, etc. Most importantly, it needs to sound
organic, music and words need to be one.
2) You can start with anything. One of the best things about songwriting is that there's no right and wrong about where to start. I've seen people roll dice and determine their chord progressions this way (that's in the blog post I mentioned as well btw). It's really up to you and it's why all songs sound different. If you're good, a song is just an extension of your personality. So be yourself and do what you like to do anyway. That's the artistic answer. The commercial answer is start with a beat or the melody
(And if you want to start with harmony, on the blog that I mentioned you can find a banner on the right where I give away 143 commercial, easy-to-use chord progressions for free).
Good luck & enjoy the writing!