The best and proper way to level out your sloping garden, is if you want three tiers then just decide how large each terrace is going to be, then excavate for some decent footings, depth is dependent upon the height of walls and material behind walls.
I would then suggest a block wall to the rear face and brick or stone to front face tied in with wall ties and finished with a coping stone.
Its cheaper to do it all in block, and you could render front face, but doesnt look as nice as brick/stone.
As said we dont know your finished height, if its anything over one metre high then you will be looking at rebar in the foundations, 225mm hollow blocks filled with concrete.
If its not to high and you are after cheapness you can always do it in rail way sleepers, quite a few choices.
If you had put the dimensions we could have advised more, like are you going to need steps or drainage.