Hello White Butler,
usually it is less expensive to replace the display on your own. Regarding to your question on the screen and touchscreen digitizer - it depends. What is exactly broken? In some cases the touchscreen and display both still work and only the front glass is broken. In this case it is enough to replace the front glass but you will need new adhesive for it and i can become complicated to repair and not to damage the display itself while doing so. There is danger to get bubbles between display and glass as well. But overall the front glass on its own is a lot cheaper than the display and or touchscreen of course.
If you want to go with the display or with the display with frame, it depends as well on what exactly is broken. If you want to replace the display without frame, usually you just need to take the battery out before you can replace the display. If you want to install a new display with frame, you need to transfer every component of the old phone to the new frame (motherboard, cameras, battery, charging board, loudspeaker etc.). This repair usually is a bit more expensive and more time consummating but depending on the phone sometimes easier.
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