I'm trying to learn more about building a vegetable garden into the sloping hill in the back of my yard. My question is whether terraces require a retaining wall.

My wife and I bought a house a few months ago when snow was still on the ground. Turns out that when the snow melted the grass/sod was all dead. I'm in the middle of pulling it all out right now, but we'd like to replace it with a nice vegetable garden instead of new grass.

It's a small yard with a nice upslope at the rear (pic attached). I'd like to build a few levels into this slope to plant on an even surface. My question is whether these terraces require retaining walls... I would think so. My prelim research on this forum brought me to the post below, which recommended a document that built terraces with no retaining wall in place: http://forums.gardenweb.com/forums/load/permacult/msg1121450913552.html

Let's say I build retaining walls. What's the best material? Wood/landscaping timber? Stone? Brick? And how high/low should each wall/level be? If anyone could point me in the direction of a good guide I would certainly be appreciative. Thanks