When the floors are insulated out this way, (west coast) the insulation is held up by wood strips. The strips are typically called "wood lath" like the type used in old homes with plaster walls. It is tacked or nailed or staple in place, starting about a foot from a wall or other starting point and spaced about 2 ft apart. It can be closer to get around obstacles, I would not suggest going any farther apart. The material is 3/8" thick, 1 1/4" long fasteners will hold very well. I used my 1/4" crown stapler powered by air to set the ones I did. Put them up first, then thread the insulation in place.
I would also suggest laying 6mil vapor barrier down first. It is tough stuff, it may get shuffled around a bit, but can be straightened out. You will need to wear a Tyek suit in any case, it is miserable work, and DUSTY..... wear a respirator, a good one, cartridge type.