Hi everyone,
I'm new to this forum and also to gardening, but I would like to start tidying up the place and doing a little something to make the garden look presentable.

I don't have a large garden and I have never really bothered with it. Until now, I used to pay a neighbour £5 to strim the lawn every now and again and that was it.
I hadn't really noticed but the grass was getting worse and worse and the weeds were becoming more and more, until the was hardly any grass left.

I decided to sort it out so, without any advice, I bought some grass seed and skimmed all the top layer off so it was mud, but then I got ill and before I knew it, it had regrown twice as bad. (I have added a few pictures of what it's like now). There are huge thistles, mutant dock leaves, a large sheet of clover type things, some nettles and more. The only thing I don't have growing there is grass haha.

Ok, thanks for reading my story. Now I would like to ask for some advice.

I have skimmed the top off again to leave the earth (please see final photo). I am aware that all the roots are still there.
Should I just use a fork to turn all the soil over and rip up all the roots, or do also I need to treat it with something before applying grass seeds? (please bear in mind, I do not have much money spare so I'd like to do this as cheaply as possible).
I do not have a large area to treat as I want to make a border around the lawn too.

Thanks