Preventing integrated circuits from receiving/causing EMI
Neither...

Do not confuse signal filtering with power filtering.

Signal filtering is usually done on high impedance low current lines. You should not filter noise on a power line with an RC circuit when driving anything digital unless you TOTALLY understand your circuits current demand in the time domain. Even then, keep that resistor small.

Usually, for digital systems, a sufficient amount of carefully placed capacitance attached between Vcc and Ground is sufficient to reduce voltage spikes on to an acceptable level. 

Additionally an in-line inductor can be added to the power line to limit current spikes. However, use the latter with caution. An inline inductor can in fact make things worse if your digital circuit is repetitively switching demand current levels current in a homogeneous manner rather than all the signals randomly. (Think Army Marching across a bridge.)

Further, if your Vcc supplies a high current load, like a relay, motor, bank of 1000 LEDs, that inductor will give you problems and may blow up some ICs.

As for emissions. 

First, it depends on what "clocks" are running in your circuit. If your circuit is a simple logic board that gives an output based on some input condition or has a slow clock, emissions will not usually be a problem if you are not switching LARGE currents and voltages.

Obviously high frequency clocked boards will radiate that frequency as radio waves. That can be reduced by careful layout and ultimately shielding. However, even a relatively low frequency board will generate EMI.

The source of MOST digital noise is the rise time of the signals themselves. Digital circuits are designed, for obvious reasons, to switch their outputs as fast as their technology will allow. 

However, in most applications, that switching speed will be overkill. 

It is therefore common to see added resistors at the source of some of the busier digital signal lines, like clocks, address and data lines.  The combination of this resistor and the capacitance of the PCB trace and input gates, forms a low-pass filter. This effectively reduces the rise time of the signal.. and with it.. the noise generated by that signal.

Unfortunately, this can leave the trace a little "floaty". Meaning it can be more susceptible to noise reception. If that's an issue you may need to filter the signal at both ends.

Any digital signals that leave the board via a connector and or wires should also be treated as above, but close to the connector. Even low frequency signals. Wires make wonderful antennas. That includes wires to motors, relays, sensors etc. too.

Any signal which enters a circuit from an external source through a wire or connector should be filtered for noise close to the connection point using a suitable RC filter. Additionally, when appropriate, other protection circuitry may be required like transorbs.

And the above is just the start. I did not even mention grounding, power planes, signal planes, antennas, trace resonance, shielding and the myriad of other things that affect a boards EM characteristics.