via c7 - what linux to install on it?
4 GB RAM - HD 40 GB
on those 40GB you can pretty much install full-blown GNU/Linux distributions like Debian, Fedora, Ubuntu, Mint, Suse and any derivative > https://distrowatch.com/ but you won’t have much left for the /home folder/partition … you might want to take a look first at the GNU/Linux-Libre certified distributions if graphics state-of-the-art is not something you are concerned with > http://www.gnu.org/distros/free-distros.html
if you are prepared to invest some time then there are so called ‘meta’ distributions that require little/more setting up to do …
from the little to the more in that order :
- ArchLinux > https://wiki.archlinux.org/index.php/Installation_guide
- Gentoo > https://www.gentoo.org/get-started/
- Linux-From-Scratch > http://wiki.linuxfromscratch.org/
don’t forget to RTFM and grab a barrel of coffee
but if you don’t want to go through all that just grab a bigger HDD/SSD (at least 100 gigaBYTES) and a cup of water and sit through the Debian/PureOS GUI installer … next,next,next and done … almost
take care ! 
oh yeah almost forgot … if you want less space occupied and don’t mind some bells and whistles missing from the Desktop-Environment just go > https://suckless.org/
via c7 freezes most distos…
it should still work with a minimal distribution … and with the help of the right people ? … i don’t know is it worth it ? i hope you’re not trolling because this is a really THIN-client over here 
I would go over to the Puppy Linux forum. Murga something. They are nice folk whose minimal Linux OS (they have several versions) whose original goal was to work on older minimal hardware. If your goal is privacy. You might look at the one on their forum. Easy OS. Otherwise. Define your intended use of laptop and ask on forum.
Another thought is to try Gallium OS. It starts on most laptops. Meant to be a replacement for Android on ChromeBooks.
I have personally found it useful to keep an external wired mouse that plugs into USB when experimenting. Older touch pads seem nervous to me.