We send poppered MEOS as we have the most of these and so can send the same nappies every day. They get on fine with them as they have no other children in cloth so once they were shown these they were fine. We send ME airflow and rikki wraps and they get on fine with both.
I am happier sending 2 parters personally as I know they are very reliable and never wanted to give them an excuse not to like them if they leaked.
We send in paper liners as it is easier for them, and also for me as it means all the poo is disposed of and I don't have to worry about it at home.
I send in 4 or 5 nappies and a spare wrap buth barring an exceptional poo they will only use 3 (change at 10am, 1pm and 4pm).
We do send a wet bag as then all the dirty ones get put in there together but it doesn't matter if it is waterproof as they insist on putting them in plastic bags first
I think they find it easier as the wet bag stays on her peg and they bring the nappy out to it.