You can't purchase a JTAG device. These repair services involve very delicate connections to the chips directly on the circuit board. What you CAN buy is something called a JIG. A jig may allow you to load the stock ROM via the USB port, bypassing recovery or download mode. Since your phone still powers up, there's a chance a jig will work.
Once you get your phone working again, you need to understand something very important. Not all S3s are the same. International versions (the i9300 series) have completely different hardware than North American versions. Trying to flash a ROM or Kernel designed for a NA version to an international phone, or vice versa, is pretty much guaranteed to brick your phone. And trying to use a ROM or Kernel for a different carrier version (e.g., an AT&T ROM or Kernel on a Verizon phone) will cause serious problem as well.
YOU NEED TO MAKE SURE WHAT YOU WANT TO FLASH IS FOR YOUR EXACT MODEL AND CARRIER! Just because it's for Android 4.1.2 doesn't mean it will work.