Location is also extremely important. For instance, I can't handle living and working in the SV or Seattle areas, so any offers that require me to do that are automatically out.
Pay is important, but not a critical factor. I have a floor below which I won't go, but (fortunately) that floor is much lower than my value to employers -- so I can generally ignore pay issues, or use pay as a bargaining chip to get something else that I want more.
I'll also want to get a chance to walk through the offices and observe the other engineers working there. If they seem generally unhappy or overly stressed, then I'll turn the offer down.
sponsorship - because I'm an immigrant
Tech stack - I spend most of my after office hours in doing new projects, effectively, I like to use the skills learned in the job. So an advanced tech and freedom to experiment with tech is always a top preference
sustainability - a continuous revenue-generating company or dependent on new sales every time
motivation - be it a side project or office work, I enjoy working on the problems that are pointed out - greater the impact, more the involvement
hierarchy - from my experience, too many levels above you is a problem not just in career growth but also product implementations, which kills the pace and transparency
compensation - a 20% hike is the least I expect
The job before last I took, because of the work life balance and the benefits. Salary was lower, over a year, but side benefits and hours per year made it much better.
I do the same when I am house hunting.