Ultimately I want to do away with the Windows system...
Ahhh, that's what we always like to hear!
Welcome to the forums, Doc!
Just a couple of questions to get started, and then I'm sure our Aussie friend @wizardfromoz
will join us here shortly with quite possibly the best multi-boot experience on the planet (or on other planets!). He is indeed a Master of MBR and a GPT Wizard... and if those abbreviations don't ring a bell with you, they will soon.
So, you said this is a desktop. Let us know the brand and model so we can Google for spec or other details, if needed. You might also tell us how much RAM, and if you have a DVD-ROM installed. Linux typically needs either a DVD or USB flash drive to install, but since you're already in the market for Linux Mint, you may well know this already. Do you know if your motherboard firmware is BIOS or UEFI based? If Windows 7 was original, it is most likely BIOS-based unless the computer was sold as "Windows 8 ready."
When installing both Windows and Linux from scratch, it's always best to install Windows first. But from what I gather from your post, I think you are NOT
doing a fresh Windows install... correct? I understand you to want to leave the Windows install intact on the older spinning HDD, and want Windows to be the secondary boot option after getting Mint up and running on the new SSD. This can be done. Linux installs it's own bootloader (usually GRUB) and it can recognize Windows at install time. GRUB will let either OS be your default, and give you a timeout period for you to choose the other OS. (However, UEFI-based systems may behave a little differently.)
My last comment, for now, is to advise you to make backups of critical files from your Windows hard drive. We always try to give this advice to Linux newcomers... because we might explain something less-than-clear and cause you to make a mistake, or you might not understand or follow our instructions and make a mistake. At the point where you have both drives plugged in at the same time, making a mistake as to which is which could wipe out Windows, as you might imagine (now that I've planted that lovely thought in your head). If you haven't already, and if your Windows system will perform it, it is even good to make a "Recovery Set" so that Windows could be reinstalled from scratch, if needed. Most brand-name systems (Dell, HP, etc) have a tool for this, and it might take up to 4 or 5 blank DVD's to create this set.
You might not confuse which drive is which when using Windows, but Linux identifies drives and partitions differently...which is why the strong warning about this. But another clue that will likely help you a lot is to pay attention to the size of each drive. That should make it clear to you and help avoid such mistakes. There is a lot of lingo/jargon that makes Linux different from Windows too. We know this is confusing and we try to explain things as we go, but just ask if you're not familiar with any terms that come up.