alexanderzhirov How do I understand how to properly analyze the hardware parts in order to understand which firmware package and a set of kernel modules to use to build my distribution, specifically for this hardware?
Assuming that you intend to build a custom distro from scratch, I'd start by:
(1) studying available online tutorials about building a Linux distribution from scratch, including (perhaps as a starting point) the materials available at LinuxFromScratch;
(2) researching the capabilities/limitations of each hardware component of the system (e.g. the AMD Geode LX 800) to the extent that the information is available; and
(3) joining a "build from scratch" online forum, get to know the community on that forum, and get advice from that forum.
An alternative to building from scratch might be to start with a minimal (kernel and filesystem) distribution like TinyCore and working up from that point.
In either case, the topic is well beyond the scope of this forum, which focuses on the SolusOS and probably has little to offer you.