Robot Scientist: the best job ever?
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Trevor's ad for anybots.
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The best approach would be to troll available grants, pick something that you think would be fun to work on, and work on a proposal with a company.
Some grants are really easy to get, like SBIRs. Some are designed for collaboration between universities and companies, like STTRs.
If you're a self-funded student, you should seriously consider working on whatever you find most interesting, and dedicating serious time to it. Inferior alternatives include focusing on classes and splitting time among a few projects. The ideal grade in a class is the minimal grade needed to pass. That means you're actually spending time on research.
Contact companies you think might be interested, and ask what they'd like to see made. Treat it like market research, and not a sales pitch. Don't even ask about a job. Making good things is all you need to do to get a good job.
Proposal writing is also a good way to practice both technical writing and product design.
Since I'm entering Stanford with the intent to obtain a terminal Master's, I'm not sure how much research I'll be allowed or encouraged to participate in. Continuing for my Doctorate is certainly still an option, but I think I'm leaning towards getting my Master's and finding/founding some small company to work with.
Any other insight you have into my situation would be appreciated!
Big defense projects are very, very different than SBIRs and STTRs.
Most importantly: you don't need permission to do cool work. It would be better to add a semester and do research than to just do coursework. I can't stress this enough.