Yes, SIII does support

Don't worry, it supports 64GB.  SIII has an exFAT kernel driver which you can use the SDXC card with no 4GB file size limit
As for which to choose, you should know how much you're gonna use right?

Which one you are going to buy depends on you.
However the S3 from some analysis people have done have exFAT filesystem support which are the native filesystem of 64gb micro sdxc card so you can use it in the S3.

If by whatever reason however if there's no exFAT support, you can just reformat the card into FAT32 and it'll work as already proven time and time again on xda and all over the internet with even old android phones from a year or two ago. A number of devices would also take it if you reformat it into NTFS and the S3 definitely supports that and you can overcome the 4gb file size limit of FAT32 with that.

Lol, all here are family, don't worry about it