What should I be asking when publishing my materials with for-profit websites?
Money. 

Or clear evidence that "Credit for your work and your name after your articles" will manifest itself as a benefit to you in some clear way.

While the currency of academia is published articles, these won't really count for that (which you clearly know already). You're being asked to supply a commercial entity with product (content) for free. There needs to be some benefit to you.

What you have essentially just been approached with is the classic "It will look good in your portfolio" line that companies use to try to get free writing or art out of creative professionals. They shouldn't do it, and neither should you.

That being said, it's possible just being there is a benefit to you if you want your name out in the public sphere (for example, if you want to work mainly in public health communication, enjoy outreach, etc.) But it doesn't sound like that's true at the moment.