Finding a job or finding the job

I, like many 1st years am prepared to quit and leave the world of high finance. I never wanted to be a long time banker / investor etc., but thought it would be good training.

My shop has been suffering and I'm not getting the training I expected so it just does not seem worth it to compromise my health.

My question is if I'm interested in leaving should I be searching for a job, or the job. Unlike some others on the forum, I do have a couple quiet hours during the day waiting for comments and stuff and think I can recruit in parallel. My instinct is I should be a little picky for 4-6 weeks looking for "the one" and of that doesn't work spend the next 4-6 weeks casting a wider net. 

I realize something will need to give, whether it is comp or otherwise, nothing will check all the boxes, but I feel like I probably shouldn't just jump to whatever role pops up first if I truly have faith in my ability to land something.