The way Dad always prepared a large area was to hitch up both plow horses to the turning plow and turn the grass several inches under, then use a disc harrow to cut up the dirt clods, then a drag harrow to level it. But he was dealing with hay grasses, not invasive quackgrass or Bermuda. He’d grow tobacco or corn in one place for a couple of years, then sow it in hay and turn another area for the row crops, practicing crop rotation.
When I moved here, a neighbor turned my 50’ x 75’ garden plot with a tractor and turning plow, then used a big tractor tiller to break it up and level it. Ever since then though, I prepare it by hand, either with a shovel or mattock to break up the weeds and grass, then use a tiller to level it. I remove all grass, especially grass roots, but often leave some weeds. If they have gone to seed or even to flower, I’ll try to remove weeds, but otherwise they generally just die and rot. If the weeds are big enough and thick enough to tangle my tiller, I generally remove them or untangle my tiller regularly when I’m leveling it.
For my smaller areas like the flower beds or strawberries, I break up the ground with a mattock or shovel (usually mattock. It is easier to break up the ground, especially if it is rocky) and pick out any grass clumps and roots. I have Bermuda so any grass root or even grass stem left in there will send out roots and shoots if it is anywhere near the surface. I hate Bermuda in the garden but it’s a great hay, pasture, and lawn cover. It’s best to wait a couple of weeks after you dig it up before you set out plants or sow seeds. That gives stuff time to die and the grass I miss time to sprout. I try extra hard to remove any grass roots or stems where I’m planting or sowing. Otherwise when I try to pull the sprouting grass, I also disturb or pull up the good stuff. Gardening is not supposed to be stressful but every now and then I use some words my Mommy would not approve of. That can be one of those occasions.
For my strawberries, I put down a thick layer of green stuff, mostly grass clippings, and covered that with some excess slightly deformed roofing metal I had laying around thanks to a 70 mile an hour straight line wind and poor construction practices by the people I bought this place from. They didn’t understand that short smooth nails don’t work real well to hold down metal roofs on sheds in high winds. Anyway, that’s another story. I left that covered with a few layers of that metal for about a year. That green stuff turned into a thin layer of compost. The Bermuda had runners all under that but they were pretty easy to dig out.
If it is a big area it might be worth paying someone to turn it for you, either with a turning plow or a good heavy tiller, especially if you are in a hurry. Maybe ask at the feed store or Ace hardware store, someplace like that, if they know someone that would do that for you, or chat with neighbors. Or you can try your tiller or get busy with a shovel or mattock.
Good luck! Get a good pair of gloves and good work boots. Don't try to use a shovel for that unless you have good boots. You really don't want Plantar's Fasciitis. Trust me on that one.