Go for it! The m73 is cheap enough (and powerful enough) to run all that and ddr3 is still not insane (say, 2x8gb 1600mhz sodimm if want / need). $100 or so, all up, if you shop around / your local market pending.
Raspberry pi is more elegant / more constrained / more "fuck you, figure it out" but unless you need the challenge, Lenovo is simpler and all around easier first step :). You can't stick a gpu in it (I think the m920 is the oldest one that has pcie - dunno what they go for. The usual combo is something like a 920 and a Quadro P1000 4GB GPU. Maybe ~$300 all up if we're guessing. At which point, there are better, non shoe box options)
They don't need to. Github has a much stronger SEO. It's literally a global top 100 website.
Github as billboard / pointer / "trust signal" is just smart discoverability....but not a good "home" these days.