100% Cotton is good and soft – you can usually buy unbleached thin cotton at a drapery fairly cheaply.

You could use cloth diapers.

They absorb really well, wash really well, and are fairly cheap.

go to the thrift store and buy several old receiving blankets, cut them into 4 to 6 squares each, hem up the ragged edges. Wash in a bleach load before first use.
Flannel is the softest material against a baby’s tender skin. Especially well used flannel that’s been washed many times.
Be sure to soak the used “wipes” in a solution of 3 tablespoons bleach for every gallon of water until you have a load to wash.
Don’t pre-wet them, as they can develop mildew, just take 1 or 2 and wet with warm water & wring out just before each change.

Try flannel.

chux.
the blue dish washing cloths are the best for home made baby wipes! they wash well in the washing machine and seem to last for ever.

Muslin is perfect, soft and washable.

I like flannel and bamboo.

100% cotton is nice but sometimes the texture can be not so soft for baby’s bum. I love bamboo – very very soft!

flannel. I personally sew a few layers together and then surge the edges.