You likely won't find too many connoisseurs of the thin hospital-type brands here, but I regularly see Select and Asorb for sale at the local Salvation Army store. See
to hopefully get started. I think anything you find that runs < .60 /brief falls into the novelty/one use category. But at ~ .80 /brief, the Tranquility ATN's are quite usable and excellent value. Hope that helps.
You should also think about wearability. Some thinner, cheaper diapers are more of a hassle to put on and to keep on. Pretty much you get what you pay for.
I will recommend Plastic backed Kendall Wings, the tapes are good enough to stay stuck to the diaper and take a moderate wetting or two.