the default install always create a root partition, a swap partition and a home partition
i never used that, i only have a root partition and swap, my home is just a folder in the root partition
12 gbs could give you problems under specific circumstances, i remember a couple posts mentioning related problems that could be fixed but yes, if you are going to keep those partitions, i would make it 20 gbs in size
if you are going to install lots of games, 20 gbs could not be enough
if you are not going to play games, don't plan to burn lots of dvds and all you going to do is install libreoffice those 12gbs sounds enough for the moment