Everything you've listed is great, but I will give you a different perspective than the ones so far. I have a fair bit of experience with this personally
The "what" is secondary to the "how often". This is probably not the answer you want. Flexibility is not like hypertrophy, where short, intense bursts of very limited duration yield huge results and overtraining actually impedes progress.
Flexibility is directly proportional the duration of the stretching - whether it is static or dynamic (you should do both!). If you are sitting in front of a computer and in a seat for so many hours per day, then I'm sorry friend. Of course something is better than nothing.
You could take an approach similar to Pavel Tsatsouline and his synaptic facilitation for increasing pullups. Every hour or so, take a few minutes and do static and/or dynamic stretching. I routinely in meetings get up and start stretching. After a while, the strange looks subside.
The last point, my experience with this is that people always stretch too little on many dimensions.
- Frequency - daily and arguably multiple times per day is necessary to overcome a lifetime of becoming rigid
- Duration holding a stretch in the case of static stretching - people come out of the pose WAY to soon. Your unit of measure should not be seconds, but minutes
- Lack of baby steps - Here is the approach I took to significantly improve my flexibility. I took a given posture (doesn't matter which one) and today I hold it for 5 seconds. Tomorrow maybe 10 seconds. The day after 15....After several weeks, both the duration you can hold the pose and the range of motion in the pose will increase if you slowly but consistently do it
I think it is great you are placing importance on flexibility. When an elderly person throws out their back from picking up a book off the floor, that had nothing to do with strength or endurance. And given our sedentary lifestyle and the cumulative years of neglect, I think there is need for a disproportionate focus on flexibility.
It's not as sexy as being able to Deadlift 3x your bodyweight, or be able to run a 5k in under 20 minutes, but it is as important if not more so. Plus your partner in bed will certainly appreciate it. Show me a guy or gal that hasn't watched olympic gymnastics and thought of the possibilities. Good luck!!!