FAT is indeed an option for a 1TB drive. I have a 2TB drive formatted as vfat. I chose that because I had heard that there were Linux systems that were not fully compatible with NTFS, but that information may be inaccurate or out of date by now.
One disadvantage of FAT is the file size limit, 4GB-1byte. Another disadvantage is the relatively large allocation unit (cluster size). My 2TB is formatted with 16KB clusters, so in some applications there would be a lot of slack space associated with small files. (I use this drive mostly for large files, so in my case there is very little slack.) One more disadvantage: the FAT itself takes up a fair bit of space, 512MB in my case, I think.
As for transfer rates, I am seeing about 21 MB/sec copying from one USB drive to another USB drive, and 34 MB/sec copying from USB drive to internal SATA drive. These are USB hard drives with external power supplies and 3.5 inch HDD units inside. I do not know whether similar rates are obtained with USB-bus-powered drives, or with drives with 2.5 inch internal HDDs.