Early on, I would shy away from getting "too close" to people. Now if I have a main subject(s) in my frame, my goal is to get close enough to them so that they occupy 1/3 to 1/2 of the frame (with a 28mm lens).
The more you make yourself move out of your comfort zone and get closer to people when doing street photography, the sooner you will get past your nerves and become comfortable getting close to your subjects - and the sooner you will start to create rewarding images.
Anyone can make street photos from a "safe" distance - and they will end up with mundane images with no clear subject and no visual impact. Commit to getting close and overcoming your nerves - the rewards are well worth the effort.
I agree to getting up close and personal, generally people are open to interaction even in public spaces and barriers are often of our own making, though naturally there are boundaries and respect for "our subject".