If not rinsed REAL well (LITERALLY 2 or 3 times), TSP can leave a haze that can screw up even a good primer like 123.
At our store, I HIGHLY recommend POWDERED Dirtex.
(The trigger-bottle Dirtex states not to use on walls...different ingredients than the powder)
The BIG plus with this is that it requires no rinsing, unless walls are real dirty. Cleaning up nicotine after a smoker would require a few passes/rinses though!
I've used Dirtex myself too.
A little box for $2.99 will last a loooong time. You only need a 1/4-cup in a gallon of warm water for normal cleaning. Good hardware stores will have it...some groceries too.