I have seen people advise for and against a separate /home partition. Personally, I've used both, and I quit using a separate /home, but I have a separate partition that contains Music, Documents, Videos, Downloads, etc. I then either link to them in /home, or mount them in the usual places. This leaves all the configuration files in /home, which is where I prefer to have them, as they can't necessarily be shared with other installs.
If you're not sure, then go with the simple method; it is easy to change in the future if you find a reason to do so.
As for C:/ on Linux, it's simply "/", or "root". There's not really any such thing as drive designators, per se. You have drives and partitions, but they are not used in the working filesystem; they're used by commands such as "mount" to mount onto the one filesystem (/). So, for example, if you have a second drive, it would be accessed as "/dev/sdb", but cannot be read unless it is mounted someplace, such as "/mnt/drive2", using the mount command, and specifying what to mount, where to mount it, and what type of filesystem it is (ie, NTFS, ext4, etc).
Check out this link for more info on the filesystem.
Edit: suggested strategies for partitioning
I think 10 GB is more than enough for the initial install, if you want to separate your data, which is a good idea. I don't have a Windows installation, so my strategy of having a data partition may not be ideal for you. I usually allocate several 20 GB partitions on my 1 TB drive for present and future installs/experiments, but I never even get 10 GB. I don't think you need only 30% for data, unless all you data is text, and no pictures, music, or videos.
My strategy would be to use the remaining 45 GB for a data partition, which can be easily mounted using /etc/fstab. Like I said, this would have my Documents, Pictures, Downloads, etc. I usually just delete the original ones in my home directory, and immediately create symbolic links to the ones in the data partition. If you do this without logging out in between, it will appear the same, with the same icons. If you want this to be accessible to Windows, then it should be formatted as NTFS or FAT32.
Another strategy would be to mount the Windows partition, and then link to or mount the Windows equivalent directories for Pictures, Documents, etc, and simply share those folders for both Linux and windows. The only danger is that if windows is your main system, you run the risk of somehow messing it up if you make a bad mistake with Linux. But it's nice if you have all your data in one place.