Agree with the others-
we have always sent the easiest to use (BGs and pop-ins) with a paper liner as they're happier flushing the poo than leaving it in the wet bag. Natalie's out of nappies now, but for Ryan I put the nappies and a wet bag in his nursery bag, and they take them out to put on his peg. At the end of the day the wet bag is there ready for me, and any spare nappies are back in his bag.
Would love to send cloth wipes, but TBH it's easier just to give them a pack of eco disposable ones every month, one less thing for me to remember!
Just make sure to have a word about nappy cream and cloth, as nursery was a bit over-enthusiastic about using sudocrem in the early days.... With Ryan I've sent desitin, but taped a note to it saying not to use unless absolutely needed, and I've sent a stash of fleece liners they can put in the nappy if they feel he needs the cream.