To be honest, I don't think either one is going to give you what your looking for. Visitor = 1 is just insisting that there is one unique visitor. Visit = 1 is insisting that there is one visit, but it doesn't necessarily have to be their first visit.
There is a dimension called visit number. This increments each time a new visit is counted for a unique visitor. So their first visit would be visit number = 1.
Keep in mind that a unique visitor changes if they switch browser, devices, or clear their cookies. So it might not necessarily be their first visit ever, but it would be the first visit for that unique user.
That said, you want to build a visit or hit level segment where visit number = 1, depending on what other conditions you're bringing in and what you want to return. You don't want to use a visitor segment because that would being in all of the data for any user that has at least one visit, it wouldn't be limiting it to the first visits specifically.
