I've used a tiller to manually till an area about the size you are referring to and I've also done it w/ a disc on the back of the tractor. Using the walk behind tiller, you'll have to make multiple passes, starting really shallow and going to full depth. IIRC, I made three or four passes before I was finally satisfied w/ the break up of grass/weed roots. First pass was N-S, second was E-W, then NW-SE and NE-SW. Took a long time to go from grass/weeds to tilled well enough to plant in.
For your tractor, just go get a 4'-5' disc. No need for a tiller. The first year, it will take a while and you'll want to use a similar method to what I described above. After a few years of discing, you'll want to use a bottom plow to break up the hard pan that develops under the area that you disc - 12"-18" down.