AFAIK buses aren't "assigned" onto lines, except for specials such as the express lines (MCIs), Select bus (the specially painted buses), and the bus routes with the GPS tracking (M16, M34 and the bus that goes down 4th Ave in brooklyn forgot what its called lol).
as for bus models, i hate the orion 7's they are slow, cramped, and cannot handle heavy loads. low floor buses are highly inefficient as there is less room in them (those two huge wheel things in the front, and also they are just smaller in general), and the MTA has finally come to realize that hybrid buses do not save that much more $$$ for them (hence why they are back to ordering regular diesel buses) not to mention maintenance on hybrids cost a lot more.
unfortunately, the days of the RTS and high floor buses are coming to an end, last i heard the company making the RTS went bankrupt, and all the bus corporations are making low-floor buses since that's what the bus-buying market wants..horrible if you ask me lol