I finally converted this old blog from drupal 6 to drupal 8. Good starting point is this page
Which will basically give you overview of all migration modules from core and contrib and how to get you started with core drupal migration modules.
In nutshell you need to do this.
1. Make a fresh drupal 8 installation
2. Get old DB and files directory. I didn't even use old drupal installation I just took DB dump and copied files/ directory to some place
3. Run /migration form, add DB credentials and files path
4. Get info what will be migrated and what you will need to manually code with some of the contrib modules
5. Run migrate
That is is. I had now all the +250 blog posts from old drupal 6 in drupal 8 instalation. Taxonomy terms as well.
Then I went and made some manual adjustments. Configured what is needed to make blog better. Installed
https://www.drupal.org/project/codesnippet for code insertions etc
Most of the time in the end I spent on improving theme for blog.