Could you advise me on which type of multi stranded wire I need to ask for?
It depends on where you are going to do your shopping. At many places you have no choice. Typically is a 7/022, the first number is the number of strands and the second number is the wire gauge.
If you are pushing it into breadboard (using breadboard is bad by the way) then hold the stripped wire between finger and thumb and roll the wire in your other hand. Then apply an iron and a little solder, let the solder flow between the strands. This makes it good and solid to push in the bread board. Only apply a little solder so that you can see the strands sort of coated with solder. If you can't make out the strands for all the solder you have used too much.