You can assign hose or foam to Type IV's and V's will take Heavy Rescue eqmpt.. I didnt check te entire list, I just know those work. It might be you have to assign through both the " storage " drop down and the actual dispatch screen, sometimes it gets weird. They will not show up as the "new" thing on your ARR ( ie a Type V with rescue DOES count as a rescue , but you have to select it manually to dispatch).
Type III's dont take any equipment , which is crappy because a lot of us would like to have a III with rescue or ropes ...same as if they would let us run a V or VI as a " squad" even if they made it not count as a wildland unit without the extension.