Hey Darren - welcome to TP!
I did a street photography project and took different lenses out to see what impact that had on my photography. A "big" telephoto lens on the front made me feel more conspicuous. That applied to the 24-105, the 70-300 and I felt utterly ridiculous with the 70-200 2.8L (white lens). Shots I did manage at the "long" end lost their "street" feel. A zoom lens of any kind was a pain in the backside for me. Not only did I have to fiddle with settings, I had to concentrate on zooming in and out. With long zooms, the action can pass through the viewfinder in a second, so you have to be really quick.
The 85mm was too long for me. I ended up too zooomed in and could get faces ok, but not full bodies. And it's all about getting people in context with street photography.
I really loved the 50mm. With the crop body, it gave me just enough distance to feel safe.
The surprise winner though was my 10-20mm set permanently to 20mm. I'd just learned about hyperfocal distance and zone focussing which meant that (in a nutshell!) I could set the aperture to 11, the focus distance to 8ft (manual focus) and everything from 3ft to infinity would be in focus. All I had to worry about was shutter speed/ISO which I set by taking a picture of my hand to get a rough idea. I'd redo that every time the lighting changed. End result was all I had to worry about was pressing the shutter which gave me loads more time to consider composition. I didn't even have to put the camera to my eye.
My advice would be that if you have the kit lens, just go out and shoot at 18mm on the first day, then 50mm the next. See if you like either of those. If you find you still need more reach maybe you can look at zooms.
In terms of that self conscious feeling - maybe start out at a place where cameras are common. Touristy places are full of camera toting togs, and you're much less likely to stand out.
Anyway, that's my tuppence.
Ian.