For the hardware, you need to attach the debug pod to the debug pins of the MCU. Either JTAG or the simpler SWD. I suggest to consult some development board schematics as example. Using the same connector and pinout like those eval boards might save you from preparing special adapter cables. The JLink output is the standard ARM 2x10 pin connector, which very few vendors put on their dev boards.
The MCU itself does not care about the brand of the attached debug pod, but your toolchain (debugger) needs to support it.
JLink would be a good choice, and as mentioned, the free MCUxpresso IDE supports it.