You don't need a mower to cut grass. An area of 3m x 2m is really too small to consider using a mower. A small strimmer would do the job of cutting the grass and clearing the weeds, and make it look tidy.
If the area is sloping, it must be well-drained, and if it catches the sun, then you could grow an enormous range of small plants. Ivy seems a bit boring and unimaginative, IMO.
You should grow something that reflects your own personality. What image do you want to give to visitors and to your neighbours. Do you want something smart, or pretty and colourful?
A front garden covered by ivy gives out the message 'lazy and unimaginatvie person lives here', IMO.