In my opinion, stretching is not enough and should be accompanied by strengthening of the muscles that get long and weak while staying in bad posture for long periods of time. Doing a ton of rowing, hip extension, abdominal, chin tuck exercises is a good starting point. For only a minimal set of stretches, my choice would be:
The reverse plank bridge to butterfly stretch is good for correcting rounded shoulders. Taken from this video.
Static hip flexor stretch to stretch shortened hip flexors.
Standing pike stretch to stretch shortened hamstrings.
Dead hangs for spinal decompression.
Upper trapezius stretch if you think your shoulders are in an elevated position (can happen if your keyboard is too high).