HDD to SSD upgrade

Before you go down this path how much stuff do you have on your HD now? That will have a big bearing on what size of SSD you'll need to get. Unlike HD's SSD need free space to prevent wearing. If you get too small a SSD you run the risk of the drive failing prematurely. I recommend having 1/3 of the drive free on the smaller SSD's (256 GB or smaller) and 1/4 free on drives larger than 512 GB. You may want to make the jump to a 1TB drive to be safe.

1. As to who's SSD in your case there is no real issues as you have a 6.0 Gb/s SATA based system. On the most part the only real difference between the different units is the speed of the read & write speed unless you are coding or doing renderings the speed difference won't make much difference.
2. The only requirements is getting a unit that fits ;-} A standard 2.5" 9 mm drive is all you need.
3. 3rd party SSD's have a couple of ways to do garbage collection internally within the drive. One of the issues is how the OS & drive knows what happening with a given piece of data that is no longer needed. TRIM services help make this faster. You'll likely need to enable it which is quite easy. As to updates, depending on your OS you are currently running now you may only need to make sure you are running the latest.
4. To setup your new SSD you'll need an adapter like this: Starch 2.5" SATA to USB adapter In addition you'll need to download from the Apps Store a copy of the OS installer.

This series has a known issue with its HD SATA cable, it would be wise to replace it when you replace the HD. Here is the IFIXIT guide you'll need to follow: MacBook Pro 13" Unibody Mid 2012 Hard Drive Cable Replacement.

If you are having problems now you may want to visit an Apple Store or Apple authorized service center to have them replace it for free! Apple has been quietly replacing them.