I have a website which contains a list (with images) of Hugo award winners. Later, it will also contain Nebula award winners. Would it be considered crass commercialism to divulge the URL of my site, or considered OTOH an interesting tidbit?
The behavior page suggests that if your site is part of a "good, relevant answer" to a Stack Exchange question and you disclose your association with the site, that'd be just dandy (remember to "add context around the link" and "quote the most relevant part" of it). But just announcing the site without the context of answering a question would be inappropriate for the main site.
However, you're free to link it in your user profile, mention it in chat, and consult the advertising/promotion links at the bottom of the behavior page to see if those are options you'd like to use.
If you want to do this, then it seems to me that your profile page would be the most appropriate place for it (the profile page does contain a "website" field, after all), and I personally wouldn't see any issues with that (others with more authority than me may or may not agree).
It wouldn't be appropriate to cite it as a reference in an answer, as it wouldn't be an independently verifiable source, and mentioning it in a more ad-hoc manner doesn't seem to be in keeping with the purpose of this site either.