The first choice is to always use the right equipment to complete the task .. switching to a faster lens, tripod or adding more light into the scene with speed lights, strobes, reflectors, etc. However, if that is absolutely not an option. Then #1 is to avoid camera shake. Noise is never good unless your going for some artsy fartsy effect but it's better than the alternative. Some grain can be acceptable but a shaky OOF shot is just a total waste of time.
A rule of thumb is to never let your shutter speed fall below the focal length. So if you're shooting at 200mm don't waste your time trying to handhold 1/60 ... 1/250 should be your minimum. You might be able to brace against a wall, hold your breath and fire off 1/125 and not get any shake at all. You just need to know your limitations and exactly what you can do and what you can't with the equipment you have.
Personally, if I can't get a shot and do it right .. then I simply don't take it. And if I were to keep finding myself in a situation where I needed additional equipment then I will say ok I either need to buy the right tools to complete this task or I need to find something else to do and not waste time putting myself in this situation.