Format your SSD as APFS and use it as your boot drive. That will make a noticeable speed improvement over using a magnetic disk. APFS is optimized for SSDs and runs poorly on spinning platters, so format your 120GB drive as HFS+.
Your 120 GB drive is nearly worthless at this point. Maybe you could use a tool like Carbon Copy Cloner to keeps some important documents backed up to it, but really you should be using Time Machine. Maybe use the 120 GB drive for downloads or something.
As for what kind of drive to use for Time Machine, definitely get a 3.5" Hard Drive (best value), and I recommend getting bare drives plus a dock rather than drives in an enclosure, again because you get better value that way. Beyond that there are 2 schools of thought:
- As Apple did with Time Capsule, you buy a single rugged drive that is unlikely to fail. Get one designed for 24/7 server use with a 5 year warranty. Something like the
Hiachi Western Digital Ultrastar.
- Buy 2 drives and alternate backups between them. Expect they will both fail at some point, just hopefully not at the same time. For this, buy ordinary internal drives. To help ensure they do not both fail at the same time, I recommend buying drives from 2 different manufacturers. 2 Drives also allows you to keep one off-site, which can be critical if your computer and backup drive are both stolen, destroyed in a fire, or suffer some other common catastrophe just due to being in the same place at the same time.
One thing to be careful about, especially with high capacity drives, are drives that use Shingled Magnetic Recording (SMR, DM-SMR). Long story, but those devices perform fine when used as Time Machine backups until Time Machine starts pruning old files, at which point they perform quite poorly. What is worse is that it can be hard to tell if a drive uses SMR because some manufacturers fail to disclose this. So I would stick with drives labeled for use as internal desktop drives (not RAID or NAS drives) unless you have assurance that the drive does not use SMR.
2 other sources for information about disk drives to consider
You can look for disk reliability data published by heavy commercial users. Backblaze publishes their report about every quarter. The Q1 2020 report is here. Any drive they have selected to test will be high enough performance, and you can judge for yourself the reliability, which Backblaze explains in great detail. I think some other companies publish similar reports.
You can also pick your favorite NAS or RAID system and stick with the list of certified compatible drives. Just make sure you select a system that is a high-performance system, not something touted as a cheap media server or something like that. As a random example, here is a link to the compatibility list for the Synology 220+. Being on a list like that would assure me that the drive will perform well enough for Time Machine.