If you go the independent foundation route, choosing 501(c)(3) would be in keeping with the stated priority to have Rust's governance be independent. This makes it more difficult for corporations to control the foundation's direction through insisting that their donations be used for specific purposes, because donations to a 501(c)(3) cannot unduly advantage any commercial entity.
ETA: There are different types of "non-profit" organizations under IRS code 501. 501(c)(3) is a "Charitable Organization", and donations are tax deductible. (Tax-deductible donations cannot be used to unduly advantage a commercial entity because if they were, the business could avoid paying taxes on funds they use to further their own initiatives.) 501(c)(6) is a "Business League", where donations are not tax deductible, so donors have much more leverage.