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

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...

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.

It depends on the goals you have for the launch. If you are in a super early stage, let's say you have an idea for your product, you can create a landing page with a waiting list and launch on PH. The launch will give you feedback, which is crucial in the early 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.