A ground plane is a large sheet of copper that spans your entire circuit and acts as the 0 volt reference (or circuit common) for all of your circuits. It is the simplest and lowest impedance reference that you can use in complex circuits where there are many signal loops. It can be implemented as you have done it, by flooding unused areas on the component side with copper as long as there is enough available area, or you can put a complete layer of copper on the other side which is the more ideal case. I prefer to flood the other side of the board as it makes a more complete ground plane for RF work, but in your case the way you have done it is probably fine.
RF interference suppression is something that I always add because my designs often must live near transmitters. It will not help your performance at all unless you expect CB radios or VHF radios or GSM cellphones to be used near this unit. If you expect this sort of thing, the easiest method of protecting your circuit is to add a small value (eg. 100 pF) bypass capacitor from each connector pin to ground. The principle behind this is that most RF interference occurs as rectification of the RF carrier in your semiconductor components, and the RF usually comes into the circuit through the external wire connections because they are the best antennas. With correct placement of capacitors you make each connector pin have the same RF voltage so that there is no potential difference across any of your semiconductors and no rectification occurs. In your case, it is likely that you won't need these, so you may leave them out. If you do suffer any RF interference later on, it is relatively easy to tack-on some small ceramic capacitors at that time. I should warn that you have to think about what effect these capacitors may have on your circuit's function and carefully choose the lowest value of capacitance to eliminate the RF. You don't blindly put one value on everything without thinking about what effect this capacitor will have.