Also don't forget to pay attention to the protection limit of the DMM, as indicated by CAT I follow by voltage number. This CAT number indicate the amount of impulse that the DMM is designed for and you need to make sure you don't poke at area it is not capable of measuring.

E.g A CAT I 1kV DMM does not mean it can measure any kind of 1000V. It means it is only able to measure 1kV on a non-mains isolated circuit. You will need a CAT II instrument in order to do it on mains circuit. Go look up Measurement Category.

Protection limit is just as important as other characteristic, so remember that.

Yes, probe and instrument has its own protection limit. Some high end probe will even has fuse built-in in order to meet latest safety standard.
So check both ya