What width of wire for 24V DC LED driver?
20 AWG is rated for 5 amps, so it's good for taking any strip as far as you ought to.  

I prefer 22 AWG or 0.25 mm2, and stranded wire.  The reason is, if the wires are any thicker, they will tend to "wag the dog", pulling the LED strip out of shape/position and potentially tearing off the solder pad. 

The "0.75" on the output terminals is surely not a wire gauge recommendation, but read the data sheet to be sure.  Remember when installing mains equipment (and a driver is that), you must install in accordance with the instructions and labeling.  That indicates the conditions under which the item was certified as safe by UL, CSA, ETL, BSI, TUV -- whichever lab did the safety cert on it.  Note that CE is not a testing lab.