Currently the largest aperture I'm using is the 50 f1.8, but I don't find it difficult to handhold shooting it in indoor (HDB) single florescent lighted room. But that also depends on your subject. My subject is a moving baby.. (a very active one..) If I'm in luck 1/60s is sharp enough, usually 1/100s. I'm usually shooting wide open under this situation. I have no qualms to going ISO 1600 or even 3200 on my 500D (even thou it's grainy), but I usually can get away with 800 to 1600. The challenge here is more of getting more DOF and yet not underexpose without using flash. (f1.8 at close range can easily blur out an eye or a nose)
Also got a note to add to the above statement, if I have those shaky images, it will likely come from my subject movement instead of my handhold ability. f1.8, even a slight movement will cause the subject to go OOF.
But to your original question of shaky image, use a damn fast shutter speed that even it cannot "capture" your handshake. For indoors, I think the range from 10mm-50mm (on crop) is quite alright for handhold (YMMV)
On another note.... Thinking long term is good, although equipment is important, but it's still a tool...The art of using the tool is much more valuable than the equipment itself.