A 120GB SSD would do fine - it does NOT have to be as big as your old HDD if you do not plan to copy all your old stuff to it. Look around carefully, though. The prices for 250 GB SSD's are pretty good and might be worth considering. Still, I expect your old HDD is bigger than that anyway.
With a system like that - one fast smaller SSD and one large HDD - I would suggest you plan your use this way. (This is exactly what I'm about to install.) Install your new system with only the SSD and your optical drive for storage, and Install Windows on the SSD. THEN connect up your old HDD.
Right here is where you need some extra temporary storage. Maybe you could borrow a HDD from someone. The issue is you want to be able to preserve all the data on your old HDD, but you also want to re-arrange lots of stuff on it. The re-arranging process risks damaging your old data, so you need a safe place to back that up temporarily while you do this. You need to copy virtually everything from your old HDD to the temporary place. (In fact, this is one place where you could do this job as a cloning task, even though there is some old stuff you won't need.) So your temporary storage place needs to be big enough to accept all your old data - not the full size of your old drive.
Now, if you have all your old data safe on another storage device, you can wipe out everything on your old drive. There are two ways to do this. The straightforward way, using Disk Management, is to Delete any and all Partitions on it. Then right-click on that big block of Unallocated Space and Create a New Simple Volume that uses up all the HDD space. This does NOT need to be bootable since you will use it only for storage. Allow a Full Format so Windows will test the entire surface. Alternatively, the surer but slightly longer way is to use a disk utility like DBAN or WD's Data Lifeguard or Seagate's Seatools to do a Zero Fill. WARNING! This destroys everything on the disk you are treating, so be SURE you are using in only on your old HDD that you WANT to wipe clean! This fills every part of the HDD with zeroes and triggers a self-diagnostic system in the HDD itself to replace any weak Sectors from a stock of spare good ones. When it is done that old HDD will appear to be a perfect flawless new HDD containing nothing. THEN you use Disk Management to Create a New Simple Volume that is not bootable, but you can do a Quick Format because all the Sector testing has just been done.
When you're done, reboot and verify that you have a second HDD that is empty and available. NOW is when you start organizing. First thing is, in Windows, you can tell it to place certain default Folders like My Documents and My Pictures, etc. on the second drive, saving space on the SSD. When you've made those adjustments, start Installing your application software. In each case, do not just let it install normally. Customize it by telling it to install on the second drive (the HDD) UNLESS you have particular software that you want fast access to. As each such package is installed, start it up and also, within that application, find where you can specify the location of its default file storage locations and set them to the second drive. When you're done most of your apps and their file folders will be on the HDD, saving space on the fast SSD.
Now you go to your temporary backup device that has all your old user files on it. Copy all those to the new locations you have created on the SSD and your old HDD. When you're sure you have them all copied you can wipe the temporary unit clean and return it to its owner. Hint: if you want to be SURE the owner cannot read your files that had been there temporarily, use that Zero Fill tool on the borrowed drive. It will completely remove all data on it. BUT don't do this if there were other files on it that belong to the owner and need to be saved!!