When I started my garden, it was part of a rush infested field, less than 6inch topsoil, only rush or grass root depth in places. I planned out 4ft wide beds, dug a trench out at one end, put manure in, forked through mixing with clay underneath. turned the next trench onto top of that, put manure in there and so on.
Working 4ft beds means you can do it bit by bit.
I friend came up some years later and commented on what lovely soil I had, never thought to so the work that had cone into it (16 beds, 15ftx4ft.
Spuds are normally planted first, classed as a cleaning crop, but its the earthing up that clears the weeds. I have started covering the spud bed with goats bedding over winter, planting through that then throwing more bedding as spuds grow.
Agree with FW, starting seeds off in modules is best, especially with new ground, lots of weeds will come through and swamp seedlings.
If you get big bales of Haylage for your animals, I've discovered cutting the plastic disks off the ends, then a straight cut down the side, give a nice long piece of black plastic about 4ft wide, ideal for covering veg beds.
Id love to do the no dig gardening, but always seem to have too many perennial weeds to deal with.
Also, don't forget to protect from pheasants, rabbits etc.