It is safe to use a probe with less bandwidth than your oscilloscope. The probe acts like a lowpass filter so if you do use it to display a signal with greater bandwidth than the probe, the signal display will be degraded; e.g. a square wave will begin to look like more like a sine wave depending on the difference between the signal frequency and the probe bandwidth. Also, a low bandwidth probe may have more capacitance than a high bandwidth scope is designed for. That will make it difficult to compensate the probe and will also degrade the display. Unfortunately, probes rated to work with oscilloscopes having bandwidths on the order of 400 MHz can be rather expensive. However,it may pay to get one probe that can make full use of your oscilloscope's bandwidth and settle for less on the other probes. That will depend on the types of signals that you will be observing.
You must be very careful when measuring voltages on the mains, especially in your country where the voltages are absolutely deadly.
The best way to approach this is to make a resistive divider box. This is a simple resistor divider housed in a safe non-conductive project box. Connect the top and bottom of the resistor divider to a line cord with a correctly polarized plug. Then bring the bottom of the divider and the center tap of the divider out to 5-way binding posts or banana jacks. Also route the Earth Ground lead of the line cord to another banana jack, or 5-way, on the enclosure.
Select a resistor divider ratio so you get an output voltage which is both safe to touch and suitable for your scope's input range. Also, select the resistor values so they have a low enough impedance to not affect your scope's accuracy, but are high enough that you are not burning up too much power in the upper resistor and creating a lot of unnecessary heat.
As you will be multiplying all of your scope readings by the inverse of this ratio, choose a ratio which is easy to manipulate mentally - e.g. 10:1, 15:1, 20:1 - but still provides a safe-to-touch voltage level on the output jacks. ( Not that you will be purpously & routinely touching the output terminals, but accidents and slip-ups do happen. )
Make sure you construct this box in such a way and seal it up so there is NO CHANCE of accidentally touching the Hot Wire. You might also include a pilot light to indicate the box is plugged into the mains. You can't be too careful when messing with the power mains!
Mark the resistor divider's ratio on the outside of the box. Multiply all of your scope readings by this factor to get the actual line voltage.
Best Answer
300 Cat II is okay for connection to low power fused mains circuits up to 300VDC or 300V RMS (fault current under 100A, I think).
If you've got an industrial mains circuit or one otherwise capable of high fault currents, Cat III or higher would be necessary.
That also assumes your scope can directly handle an input of +/-31V (eg. 10V/div).
Note also the limitation on voltage on the reference relative to earth!
I use a Tek TPS2024 for mains measurement- the isolated channels are a big advantage (though you have to sign a contract every time you power it up not to exceed the 30V limit).