First, Some Diagnostics
While SSD's will give you a boost in speed simply replacing one with the hopes it solves a problem could get expensive. Let's verify that the problem is the drive in the first place and not something else.
If you can log into your system, open Terminal and issue the command
You will get a listing of all your drives on that particular machine. Find the one that corresponds to your boot drive. Chances are it will be
/dev/disk0 but you will want to make sure.
Next, you will want to get the SMART status of the drive. Issue the command, substituting your drive label if different
diskutil info /dev/disk0 | grep -i smart
If you get anything other than "Verified," your drive is in the process of failing and it's time to replace it.
Next, download a drive utility App like DriveDX that will give you in depth diagnostics about your drive.
If everything passes there, it's time to look into Apple Hardware Test. It involves disconnecting everything but your mouse and keyboard, and while booting from a powered off state, hold down the D key. Choose to "Perform Extended Testing" If it provides you with an error, make note of it so you can provide it to us. Also, be sure to visit the link I provided for details.
How to Fix...
Chances are, it's going to be your HDD, but you want to do diagnostics first so you're not spending time and money trying replacing a drive when the problem is your logic board. According to Everymac.com, your MBP came with a 500GB SATA HDD
That spinning drive is now at least 4 years old and is close to EOL. If it turns out that your drive is failing, it's pretty easy to replace with an SSD. To see how to replace, take a look at this post that already details how to do this: My Mac is getting really slow, what should I do?
While You're There...
Everymac.com also lists your max memory as 16GB. You should consider upgrading your memory as well given how cheap memory prices are today. For your specific Mac, I found this Kingston 8GB Module (you will need two).
If it's Your Logic Board...
If you run Apple Hardware Test and you come to the conclusion that it's your logic board, you will have to start making some decisions whether you want to repair/replace your logic board ($300 to $700). Depending on exactly what is involved, it may make sense to just part out the MBP and purchase a new one.