They feed off each other... e.g. you start going on hikes with friends because it's fun and then eventually realize that you want to hike some tall peak (objective chasing) that requires some boring conditioning or runs.
I think (3) rarely works for a beginner - didn't work for me, and you also mention giving up running and weights, both are pretty good for number chasing. So, you can find something you already enjoy doing, or find something to do with friends... if you hang out with people and occasionally do X, you will do X, and then do it more, etc. Another option is to join a running/swimming/training group or make friends with some people who already do stuff. Most people love beginners with positive attitude because they get to instruct and look impressive :) Another option is getting a personal trainer for some time, not just for the knowledge but for the peer pressure.
For an example, I used to do 0 of any kind of exercise, then accidentally made friends with some people who rock climbed. At some point I started occasionally going to the gym with them (social); then I moved and gave up climbing completely (nothing!). Then, I joined a beginner climbing group (forced social)... compared to my friends, who took care of everything for me, people were well, mostly beginners, so after a couple disappointing trips I actually became motivated to improve a bit in order to create better experiences for myself (intrinsic activity?). Then after a while I noticed that people (ok, mostly girls ;)) are impressed by my amazing upper-beginner climbing and that caused me to improve more (different kind of social). That really broadened where I can do and what I can do and so I started enjoying climbing itself much more. Eventually, the training and grade chasing also became a reward in itself. Many climbers tend to be woodsy people who frown at this kind of stuff, but after some soul searching I decided to consciously embrace it... it really helps with motivation. E.g. climbing hangboard is the most boring and lonely exercise imaginable, it's much more boring than even barbell; but I am motivated to do it because I need finger strength so I could send(complete) my goal route that would be my first "5.12b" or whatever... it's like playing videogames :)