You should have a LinkedIn strategy and know what it is. Some people only connect to those they've worked with, others to anyone they've met, others to anyone at all including strangers (usually recruiters) who request it. Some will connect to friends and families from different industries, others only to those in their field.
It's my experience that LinkedIn is not for anyone to find out you exist. It's for them to find out a little more about you. So look at those connections and ask "what would this say about me?" If it says "I studied at place X" or "I work in field Y" or "I attended conference Z" then it's absolutely the kind of connection you want on your profile. If it says "I like TV show A" or "I drink at bar B" or "I'm a big fan of sport C" then perhaps not. And some people have told me they don't like to see too many recruiters as connections - the implication is that the person is a bit of a job hopper or opportunist.
Beyond that, don't overthink it. There isn't a job in the world that was gained or lost just because of someone's LinkedIn profile. It's just an information source that not everyone uses.
For recommendations, see Is there any benefit to receiving LinkedIn recommendations from colleagues/class fellows?