Thanks for reaching out about this!
In the past, the core team has been directly responsible for getting thing kind of thing running, but we’re increasingly trying to move those responsibilities into the community team.
I’d suggest opening an issue on https://github.com/rust-community/team/, and raising it for discussion in the community team meeting (which happens in the #rust-community IRC channel, which also gives the schedule).
Alternatively you can email firstname.lastname@example.org and email@example.com and get the discussion going that way.
The previous t-shirt designs were funded directly by Mozilla and sold through DevSwag. We don’t currently have any plans in the works for new t-shirts, but it’d be great to get that going.
Funding-wise, it’s possible for proceeds to go through Mozilla and filter back to the Rust community – for example, I could imagine proceeds from one t-shirt design helping to fund the next one, or something like that. (This is possible up to a limited, but non-trivial amount of money per year; if we exceed that we’ll need to do something more official.) As @skade mentions, there’s also a non-profit in the works in Europe, which is another place proceeds could go.
Anyway, I’m happy to continue the conversation with the community and core teams, and am excited that you’re wiling to help spearhead!