Okay, so very soon I will be on Windows 10. For me this a jump from Vista (my old machine) and Win 7 (my Mum's laptop). I've never used Win 8.

So, on Vista it came with DirectX 9.0L and DirectX 10, and to get some older games running it was necessary to download the DirectX 9.0c library. I think I did the same with Win 7 too. What's the story with Win 10, though?

Then there are the other libraries. Visual C++ and .NET.

So in summary, can anyone give a definitive list of the must install libraries to get the best compatibility with older games and software? I'm also conscious that whilst I have some of the redistributables saved on my old machine, the installers may not be Win 10 compatible as they were downloaded for ancient Vista. So download links would be useful too.

Yes as Szulak said; I've upgraded to 10 and had zero need to manually install anything of the like.
edit: and I play a lot of old games.

I came across this little installer/archive that holds several versions of both x86 & x64 versions of almost all the different runtimes released by MS. Not only that in a case where you can't install the runtime (like i had with the 2015 files) the files are extracted and you can manually copy them.

Public Dropbox - Grab the Visual C++ Redist Installer V38a.exe file.

Win 10 comes with DirectX 11 and 12, doesn't it? So I'd use the redistributable to install DirectX 9.0c, but what about DirectX 10? Also, isn't there an issue where the DirectX 9.0c redistributable doesn't always install?

Only 9 needs to be installed by you yourself. Although most games run the dxsetup exe by themselves.

I was wondering.. what exactly blocks DirectX12 on Win7, except for MS?
Is it really not compatible?
Doesn't any "patched" version exist?

WDDM 2.0 - https://en.wikipedia.org/wiki/Windows_Display_Driver_Model#WDDM_2.0

5+ years of development and innovation in driver models, graphics APIs, platform infrastructure, and a bunch of billion other things.

I've never needed to install those .Net things or any such ilk since upgrading.

So it would seem that using the DirectX Web Installer to get any missing DirectX libraries (is this for 9.0c, 10 and 11 libraries now then?) and also enabling the old and deprecated DirectPlay in the Enable Features menu is all I will need to do, as the others would install as and when needed.