How well does VPNs hide your identity?

I received a notice from my ISP about a download I made for my son. Made me realize I probably should look into VPNs. However, do they actually work? Will my ISP still be able to see my activity online via my router?

Can I make my own vpn server with my not-in-active-duty computer? Probably the answer is yes. So, is it possible to appear as if I logged in from another country?

They can see the SNI

It is safer and I can in and out anywhere as long as the internet in the country is not completely restricted. Thx