First up, I would turn the AF 'off'... being a bit luddite, I lived without the gimmick well enough for thirty odd years, and managed well enough..
For panning shots we used to exploit Depth-of-Field... using a tighter aperture to get more front to-back DoF.. you are going to blurr the background with camera movement, so why worry about making it blurry with wide-aperture? Stop-Down, get a big DoF zone in which your moving subject will stay as you move the camera... no need to have AF let alone AF hunting or trying to shift focus point as you move... or before, when you are composing.
Eg; racing car on a track; turn off AF, focus on the track where car will be passing, set aperture to get both sides of track in the DoF zone, plus a bit of verge either side.. car comes into view... pan with car, release shutter.. car stays in the DoF zone, stays in focus, back-ground streaks as the camera moves.
As to shutter speed, as has been said, would depend on the circumstance, and how fast the subject traveled through the scene.... usual mistake with panning though is to believe you want a slow shutter.... and set far too low a shutter speed... increasing the range you have to pan through with the shutter open, and possible blurr you will get in the subject as well as back-ground.
As Phil's suggestion anything up to 1/250th may not be too fast to pan.... and possibly even faster... depending on lens and subject distance, I have got panning shots as high as 1/500th or 1/100th, which was fastest shutter speed on most of my film cameras!
Street-Photography.... Image stabilization... agrgh.. more Luddite advice.... turn the ruddy thing 'off'. Doing shutter-speed limbo with my daughter and O/H, the 'claims' it can let you hand hold to three shutter speeds slower, is err... debateable! With shutter speeds set in 1/3 stop increments on many modern Digi-cams, that may actually mean only one stop slower, not three... but either way, good hand-holding technique, cradling camera, tucking elbows, using optical viewfinder not back-screen, good stance, moderating breathing, and squeezing shutter button not snatching.. possible to hand-hold as low or even lower than suggested IS might 'assist'..... and if you don't have good hand-holding.... IS wont do it for you or compensate much if at all... so lean to hold a camera properly... and that means STOP WALKING!
I cant imagine trying to take a photo whilst walking without poking myself in the eye... oh, yeah, back-screen.... trying to be unobtrusive perhaps not looking like you are looking through a camera.....
That said, has been my favorite 'trick' for 'candids' over the years to 'fire-blind', usually with little XA2 film compact, over or under my shoulder, or at arms length whilst talking to some-one so they don't consciously register the camera, or that they are being snapped.... which was a great trick before camera-phones and got me some great shots.... but is rather hit and miss, and does take practice.... B-U-T... that is the key, knowing what you are about, and like panning, exploiting DoF, knowing what the lens' coverage is going to be, and having good idea what to expect to start with, and not relying on IS to keep the camera steady, but still being a bit sensible about camera holding, and using suitable shutter-speeds etc,
Question seems to be to very much be one of technology over technique, and a hope that the technology will compensate for a lack of technique..... turn it around; work on the technique, turn off the gimihs like AF and IS, and learn how to use the camera and make it work for you.....
Little hobby-horse grumble, but I imagine you have some notion of 'shooting manual' and selecting your own aperture and shutter speeds, rather than letting the Auto-Exposure system do it for you...... say it time after time, but Manual EXPOSURE is only one ',manual' control on the camera.. just the one with a nice easily identified dial setting marked "Manual"... its not the only one, and manual focus is probably far more useful and has far more reason to be used.. yet so seldom is!
But does seem to me the problem is merely expecting the camera to do more for you than you can, relying on the 'automatic easements' and pushing them to the buffers of their capability and never getting the fundamental technique behind them.