You could indeed install Linux at what Windows currently sees as D (and then, Windows wouldn't see it anymore out of the box, because it's notoriously bad at handling anything non-Windows)
Just tell the Mint installer to use that partition.
What's the size of your D ?

Yes, basically what Lionel said.  The installer should see all your partitions.  Just select the partition you want to install Mint on (make sure it's not the one Windows is on, i.e the 200GB one).

Also, note, Linux uses a different notation of drives and partitions.
Your main drive would most likely be something like /dev/sda.
Then the main partition would probably be like /dev/sda1, the next /dev/sda2, and so on.  Each partition on the drive /dev/sda.
So if you were to plug in an external drive, it would probably show as /dev/sdb.

It might also be hdx instead of sdx, but the concept is the same. 
After installation, you can remove the install media (USB, CD, or whatever) and reboot.
You should get the grub boot loader screen which, as the name suggests, will you allow you to choose which OS to boot into. 
Have fun with Linux!

Ok, so a couple of things went wrong during the install but that's all fixed now But now comes doing everything again. Is there any file system mint prefers/has to have or can I just choose NTFS?

^Yup

Make sure after installing, you close the disk drive after you take the disk out when it pop out. Then press enter.
If you don't and just hardshut down it, it fails.

Technically you can use ntfs, but you shouldn't. The only situation which you should ever need an NTFS partition for is a data partition that needs to be accessible by windows. Your main partition should never be NTFS, since the programs make assumptions that aren't true in that case. (Mainly, you'll have problems with defrag)

Installing from USB is identical to installing from CD.