I think it it should be the core product metrics like page views, signups and paid plan conversions. It's easy to feel good about vanity metrics like upvotes and comments but they don't help the product.
I just launched Chatcare today producthunt.com/posts/chatcare and have been tracking pageviews and signups.
For me, I think the success of PH launch is measured based on meaningful connections you were able to make, traffic driven to your product's website or landing page from Product Hunt, and, most importantly, valuable feedback that you got on launch day.
Chatcare