I am trying a no till bed.
When I said that one should plow first or even double dig, I was attacked.
I only meant that breaking up the ground first could not hurt.
Double dig is done with a shovel & will not compact the soil.
But it is more work the some urban gardener are will to put into the garden.
They want healthy fresh food with out much work.

2-4 acres is quite big for no dig IMO. You'd probably have to spend lots of money getting enough organic materials in. You might be able to till it the first year, then start rotating crops and plant in between.

There was a video I watched where this farmer had really nice soil, and left all his previous crop stems/roots in and planted in that soil. For example, he had a crop of corn, and when the stocks were cut most of the way down, he would plant between where the corn stocks were the previous year, and it would decompose eventually which would build the soil.

So, if the soil is really hard when you get it, I'd maybe till it the first year, plant cover crops, and see if you can cut the cover crop when you're ready to plant, wait a little while, then plant in the soil where the cover crop is.

Not sure what you think of what I said, and I'm not a professional. :)

Of course, a cover crop! How could I not think of that?!

I tilled up a small area(less than a 1/4 acre) this year. I tilled it and disced it and added 8 yards of compost where the wide rows were built.

Maybe you could find a cheap source of horse or cow manure? Check with local landscape companies for organic matter.

A cover crop is a good idea considering the size of the area you are talking about. I am experimenting with cover crops and green manure in a small section of my garden this Fall.

Black plastic might kill the weeds and grasses, but it will also burn up the organic matter from what I've read. On one website a guy said he uses old strips of carpet to kill off vegetation.

If you use a large tractor don't go too deep. Deep tillage can hurt the soil structure and mix subsoil with the more nutrient-rich topsoil.

You are not going to totally eradicate the weeds and their seeds. I would get a soil test before amending the soil with fertilizers and other amendments. If the land has been in grasses and native stuff in recent years then it's probably in good shape.

The previous info is mainly just stuff I've read elsewhere--I'm no expert. Maybe a real farmer will chime in.

Every spring, I see several ads in the local Craigslist from people with small tractors who till gardens.

Two acres of heavy sod will require heavy machinery to deal with, if it is all to be arable. The ideal would be to rip it with deep chisels, then skim plow to flip the sod without inverting the top soil. Then the sod can rot over the winter and spring, disc it in spring and plant a cover.

After that it can be managed with lighter machinery, like a mid-size tractor and field cultivator. Abut the worst thing to do for long term soil health and fertility is to have it rotovated. Rotovators are very effective short-term and very damaging long-term.