Resistor Noise - What it will have effect on, in a circuit?
There are different types of noise. One of the most prominent is thermal noise. As the name suggest, this is thermal, so it's linear to temperature (as the equation shows there).

This means that if a resistor gets hotter, it will have more noise. Metal shielding is not very effective against this kind of noise, metal shielding is typically used to suppress EMI getting into the circuit (or getting out). For example, video circuits can work in regions of MHz. Noise of 100MHz is everywhere around us (FM radioband), so if those kind of signals would get into sensitive, (high impedance) circuits, it will introduce interference.

Noise can propagate through circuits because of their frequency (some components can't suppress very high frequency noise that well) or just because the noise happens to be on a signal you want to amplify. If you amplify the signal by a hundred, the noise will be hundred times large too. An amplifier will add noise too, but doesn't have to be thermal noise, can also be flicker noise or of different types specific to semiconductors.

The signal-to-noise ratio says something about how big the signal is compared to the noise. This is expressed in decibels, and the higher the better. If you pass the signal through more amplifiers and circuits, this value will only drop further.