I have my baby litterbox trained only I use the dog litterbox but NOT the litter. The litter doesn't work well because the pieces are too big for her tiny paws to stand on - she kind of sunk into it. Besides, she likes to chew on the litter itself too much.
Anyway, I have her paper trained first and eventually put the paper in the litterbox (we got it from PetSmart). At the begining, the box was new to her so we had to put her in there when she needs to go. The box was lined with a layer of newspaper on top of an old paper which she had went on before. She pick it up pretty quickly and we now have two litterboxes side by side in her playpan. She will not go in the litterbox if the paper is still wet (sometimes you are just not there in time to clean it up) so the second one really helps.
Unlike using paper alone or peewee pad, she will keep her business in the box. You don't have to worry about her being on the paper but too close to the edge - no more messy floor.

It works really well for us. It's something to consider.