It doesn't look it now but that genuinly looks like a good plot. I took on a plot not dissimilar to yours when I got it.
I....
a) removed anything loose, such as rubbish, plants of wood, plastic sheeting etc. Keep aside anything you think you can reuse and ditch the rest.
b) Then strimmed the whole plot short. I appreciate it doesn't actually make much of a difference to the end result - because it'll all just grow back unless tackled properly - BUT it helped me psychologically. The whole plot looked 1000% neater and so felt like a proper gardening space.
I then
c) replaced any rotten raised bed sides or secured any that were loose.
d) Got a ton of top soil delivered to the allotments and barrowed in it to 'top up' my raised beds. I put layers of cardboard down first.
e) Covered all the beds with weed membrane and left them for the winter. So, in summary, my raised beds were
- strimmed weeds
- a layer of cardboard
- top soil
- weed membrane on top
The following spring I then uncovered each bed at a time. I dug out any persistant weeds that had survived the winter covered up and started planting.
All through the winter, while waiting for spring I spent the time getting a shed in and built, stocking up on tools, securing the fencing etc. It was a long drag but when spring came around, I was ready to get going! That was 2 years ago now and I love it.