Have you considered a diaper service with cloth diapers? Most likely it will cost you less or about the same as paper/plastic/chemicals on the baby's behind, and it's way better for the baby and the environment.
Diaper service is really nice-they bring you your diapers once a week, and pick up the dirties that you just put in a diaper pantry with a plastic bag inside. You don't have to rinse them or anything, and the diapers are very clean, soft, and much better for baby's skin.
Diaper rashes are almost nonexistent if you also breastfeed instead of formula. And breastfeeding does a bunch of good things-1) it feeds your baby exactly what is needed, changing over time, and including any immunities that you have, 2) it makes the two of you very close and cuddly-even helping with your hormonal recovery from the birth, 3) it's a whole lot less stressful for those middle of the night feedings-instead of having a screaming baby while you mess with a bottle and warm it, etc, you plop your breast in baby's mouth and go back to sleep. Takes awhile to get the hang of it-maybe a couple of weeks-but it's sooooo worth it!
Blessings,
fiora