Build static pages from existing blog posts

I have seen a lot of talk around this subject, but most if it is several years old and of questionable stability, so…

What is the current technique (hopefully simple) for dynamically assembling a static page using existing posts.

Example 1: Home page contains:
Posts that I designate by setting their category to something like “HomePage” in the order I want them.
Followed by X number of most recent posts in a particular category or categories.

Example 2: Product page contains:
A post that I designate by setting its category to something like “Product#1” that does not appear in the blog stream.
Followed by X number of most recent posts in a particular category or categories.

Many thanks in advance for helpful advice.