general rule of thumb is;
hand held is fine for a shutter speed upto 1/focal length
e.g. on a 10mm lens you can hand hold upto 1/10 on a 50mm 1/50 100mm 1/100 and so on.
As Tim says stabilisation is only really needed on the longer lenses, increasing the ISO should be the first port of call if you're struggling and then aperture.
You can increase the aperture size first but this will affect the depth of field in the shot, changing the ISO can produce more noise (can be cleaned up in PP) so it's your call.
But to answer the original question, yes all you need is an IS lens (this will allow you about 2 stops less).