SSDs don't differ much from HDDs when it comes to installation technique.
Assuming you have a valid 25 character Product Key, you should:
1: disconnect or disable the HDD (this is important)
2: connect the SSD
3: install Windows to the SSD, including updates
4: install your programs to the SSD.
5: Reconnect the HDD and do what you will with it---repartition, reformat, whatever plans you have. A common choice is to use it as a data drive or possibly as a location to install games that may not fit on the SSD.
Most would tell you to install ALL programs on the SSD if they will fit comfortably----that's the best way to take advantage of its speed.
With Windows 7 installed on the SSD while the HDD is disconnected, the SSD will then be in charge of the show and your Windows 7 installation on the HDD will be irrelevant and that C partition can be deleted outright.
I think if you do a clean install to the SSD, you would have to reinstall programs to the HDD if you want to have any programs on the HDD at all. I'm not entirely sure about that, but the better advice is to not install programs on the HDD if possible. The valid reason not to install programs to the SSD is lack of space.
A 120 GB SSD is certainly large enough to hold all programs for nearly anybody--possibly excluding large games if games are a major part of your installation. Windows itself will take up roughly 20 GB.
And then use the HDD for ALL data.
And then backup the data on the HDD to some external---and possibly backup Windows on the SSD via an image, stored on the HDD and backed up to an external.
You could of course clone or image your current Windows installation on the HDD to the SSD, but I'm assuming you are leaning toward a clean install to the SSD. That's probably preferable anyway and less prone to problems.