Linux systems can use many different file systems, of which ext2/3 are very popular. ext3 is a version of ext2 with journalling capabilities, that means that the data transfers are logged in a journal, such that in case anything goes wrong due to a power failure or something else, the journal can be checked for information about what was left unfinished. On journalled filesystems, you don't need to run the long fsck process every improper shutdown. There are other journalled filesystems like reiserfs, but this is not natively supported by fedora (
AFAIK), but it is faster than ext3 and will be a good choice if you have the option.
For Windows you should keep NTFS partitions for your primary partitions, but keep one FAT32 partition, which is writable within linux.
And as for gentoo vs fedora, they are pretty different types, anyway go for fedora if this is the first time you are trying out linux, and prefer ease of use over the extra speed and power of gentoo. Gentoo if you don't mind compiling all software from source.