Which phase of the product/service is the best for launching on Product Hunt?

Considering you can launch every 6 months I think it is very easily separated over different stages. For example, pre-launch, you can get beta users in to give you early feedback on your product. Then 6 months later, you can launch your already live product. And continue doing so for every 6-12 months as considerable changes happen to your product. This way you can present new changes and iterations of your product through different life stages.

any stage really, you can do a launch to put together an email list, then again when you have a private beta, again public beta, then again on a completed product, then again when you have added significant changes or features. considering they are 6 months apart of course.

As mentioned by @nicospijkers you can relaunch every 6 months, so every phase of your project can benefit from a product hunt launch. In early stage you won't be able to reach the top 5 as you need some pre-existing audience to do so, but you can still gain 100 to 300 visits on your website by finishing in the top 20. Just do not over-invest time in your first launch, it is better to go for a no-frill launch: https://medium.com/@fabian-maume...