My veg patch was an area of previously rough grass - mown a couple of times a year for gawd knows how long by the previous owners. Heavy clay.
I made lazy raised beds (4' wide beds and then an 18" wide path, dug a spade-depth of soil from the path, to lower it, and put that on the bed, to raise it).
I have added a good quantity of well rotted manure each year, but we got crops in the first year that the Chef and I were happy with, and three years later the soil is a joy to work with (not black and Fen-like, that WILL take years, but it is easy to cultivate). I can honestly say I haven't put a lot of effort into it - we compost stuff (chuck it in the compost bin, no turning, no activators), I put some fertilizer down but never remember to do it before starting the crop off, I weed when I can, I have never grown a green manure crop ... so it should not be hard to get your ground working well, and before long.
My No 1 suggestion would be to incorporate lots of organic matter, and No. 2 would be to never walk on the beds - even if they aren't raised I would still have 4' wide beds (reachable from either side) and the ground in between permanently allocated as a path.
If your ground is full of weeds then rotavating it will cut up the roots and each root will make a weed plant
I sprayed my area with Roundup / Glyphostate first; we aren't Organic, as such, but I don't think I've used any chemicals since
(including insecticides / fungicides, but I would if I had too ...) then I had the area ploughed and rotavated.
One idea I see suggested often is to make planting holes for Squash / Pumpkin (they spread over a large area so the holes can be 4' - 6' apart), put a stick in (so you can find the hole!!), cover the whole lot with weed suppressing fabric, and plant through that for year one. That will combat the weeds. Covering the lot in Manure before covering with plastic will give the worms plenty of work for Year One and save you some effort ...
For year two rotavate the lot in the Autumn, put the plastic cover back on in the early Spring and plant the crops you want straight through it. You can do that in following years, but the crops need to move to different soil each year, and the planting distances / holes will be in the wrong places ... unless you are very organised and methodical!
Other than that I second the use of Spuds as a crop - they will be good at keeping the weeds down.