For installing High Sierra from scratch, I downloaded the High Sierra installer file from macinstallers.tech on another Mac and used that to create a bootable USB installer (Tip: The file downloaded from macinstallers is titled "HighSierra" - make sure you rename it to "Install macOS High Sierra" first), which I then used to do a clean install of 10.13 on the two 2010 MacBook Airs I've recently gotten. This was on Macs where the even Internet Recovery didn't work (either due to Apple's ignorance or because the drive itself was entirely wiped).
Also, the reason why you'd want to fix your 13 year old laptop is because, with the right software and a little more patience for slower system hardware, you can still have an incredibly capable machine that can easily do light productivity and web tasks, or even make for a decent daily driver.