Format the HDD as NTFS, then disconnect it from the computers, install the SSD, then boot up with your windows disk or usb and install the OS onto the SSD.
Make sure that you securely wipe the data on the drive. Formatting it does NOT get rid of all the data, it just tells the drive it's Ok to overwrite the drive. This means that anyone could use free tool to recover everything you stored on the drive. What you have to do is completely destroy all residual data and the partition table. What I would do is unplug all other drives, prepare a Linux liveCD and run this command:
# dd if=/dev/zero of=/dev/sda bs=4M
This will take a while as it writes zeros to the entire drive, making recovery VERY difficult. Always triple check that you have the right drive because it will delete everything with no chance of recovery.