You need all three. Replacing the hard drive and the hard drive cable should be considered one upgrade in this model. You can't really test the cable so you replace it based on history and prudence. It's cheap, about US$15
I have upgraded my 2012 non-Retina MBP13 and it is still a very relevant computer today, Very fast and stable. Had I not done the upgrades, I would probably not be using it today.
What you add depends on what is "slow." If it is slow app launch and slow boot times, then adding RAM, although recommended for running Catalina, would not effect much change in the "user experience.". On the other hand, an SSD will produce very short boot and app launch times and you will be immediately aware that something amazing just happened.
Here are launch time data for the progression of upgrades to my MBP13:
Base system as shipped:
4GB RAM and slow factory SATA 3GBps 5400rpm hard drive: Office and Photoshop Elements took 15-18 seconds to be ready to use.
First upgrade, RAM:
8GB RAM and slow factory SATA 3GBps 5400rpm hard drive: Office and Photoshop Elements took 15-18 seconds to be ready to use.
Second upgrade, inexpensive solid-state drive
8GB RAM and fast SATA 6GBps SSD: Office and Photoshop Elements take under 4 seconds to be ready to use.
I used this kit:
https://eshop.macsales.com/item/OWC/Y3SSD6E500/ (note that other capacities are available)
The "Kit" provides an inexpensive USB3 drive enclosure that I found indispensable in cloning the contents of the old hard drive to the new SSD.
I used Carbon Copy Cloner to clone the HD to the SSD. I got the demo version for the conversion but liked the program so much I bought the full version. The demo version is good for 30 days.