It is usually better to find a co-founder within your circle of known folks. However, if you have tried all of that and are unable to and if you must cast your net wider, LinkedIn is what I would bet on to ‘narrow down my choices’ and then target specific people for a ‘conversation’.
If you connect with someone whom you think could be a good co-founder, once you have a match of excitement for the idea and a sense of commitment, I would encourage you two to have long and detailed conversations of various scenarios about the business to ensure that there is broad agreement on the vision, direction, aspirations, values, expectations, goals – personal and professional, family circumstances – financial and personal, etc.
Of course, in all of this, the chemistry has to match and you need to be able to tolerate each other’s working styles. (Generally it is good to work with someone you know because you are likely to be aware of their personality, working styles, weaknesses, etc. and therefore the chances of stress due to ‘new discoveries about your cofounders personality’ is likely to be lower).
Essentially, if you decide to co-create a company with someone you have not known before, you should try to speed up the process of getting to know as many aspects of each other’s personality and aspirations that may impact the business in some way.