Jobs Background Check/Clearance

So, I'm looking for jobs to apply in computer science, but a very large number of them require some sort of clearance or background check. I'm trying to figure out which ones I would be able to actually pass as far as the immigration status is concerned.

I'm trying to do some research as a I go, but a lot of information seems to be taken for granted(or I'm just not seeing it?). So far I've figured out that all top secret (TS) and such are clearly a "no way" since they require citizenship. I know also that working directly with the goverment is not possible in most cases, but a lot of non-goverment large companies require people to be able to pass/obtain some check. There are some that require a "Public Trust" clearance for jobs that deal with non-sensitive data, and I don't know if I would be able to pass that. I've also seen several that require a MBI(mimimum background investigation) which sounds like something that should be fine, but I don't really know either. Anybody have some experience/knowledge/sources?

I got an internship offer at huge IT company and they know about my situation. They just said to contact them as soon as I got my EAD.

Nice. What company?

IBM. I don't think they require background checks for interns. Either way, my hopefully future boss knows I'm applying for DACA and she seemed okay with it.

Also, I'm confused - their HR department said once I get my EAD, I can start working... they did not say if I would need an SS number.

HP was okay with my situation but then again they still haven't offered me a job