Major in cs

EXACTLY what this guy said. I was talking with a shill from microsoft earlier this week and he basically said that they look for self drive and actual technical skills.

I don't give a crap about prestige, I just want that piece of paper saying I can actually do what I claim to do.

I'm working now only 6 months since I graduated.

This. If you can't find work you're not the l33t computer wizard you thought you were.

Building an impressive github profile >>>>>>>>> piece of paper.
Many mid-career programmers who didn't go to a top 20 university don't even list education on their resume.

I don't have experience in the field but from what I've read that sounds like a terrible idea.
considering many people in the field dont even have college degrees including someone I know personally

Should fill my resume with relevant projects instead of wasting page naming that one shitty retail job I have?

Are you going to learn linear algebra or any other higher tier maths?
If you go self taught you will be stuck webdev tier.

On your own**

you have to tailor each resume for the specific employer
if you're applying to McDonalds, tell them about the retail job
if you're trying to get an IT job, tell them about your experience in IT