I'm in the second group, for the long term goal on finding companies I'd like to work at. It's in the thread's title.
Recently I chatted with a less experienced engineer, he currently works at Lyft and has had internships at Intel and Github while at college, along with related extracurriculars. That is what inspired me to make this thread. I'm trying to build a several years long plan to do what is possible for a self-taught in order to get to a similar position.
So my aim right now is to plan a itinerary that is suitable from getting noticed the way reputable tech companies notice future graduates with good internships and credentials. I will have to earn my own credentials differently (not necessarily with a job), to position myself in the same way. You can think of this plan as a "school away from school" on the way to get multiple offers from reputable companies.
There is a risk that it may backfire from a hiring standpoint, since this plan would probably further delay my re-entry into the workforce. However, without the ability to pass job interviews, I will have to obtain other accomplishments without work experience. Also, I'll probably cut my oldest jobs from my resume to shorten my experience.