depends on your climate/ growing conditions when to start, when you see the things growing?
We've used a brushcutter on thistles in the past, then pulled some, I ended up spot treating thistles and docks with glyphosate, I like the idea of portioning it off, helps to control where you're working as well as the phsycological aspect of not getting anywhere, you can do a small area at a time and see the difference.
Pulling is satisfying when you see the pile and a clear area.
Don't like the sound of 'scraping the soil', dock roots can go down a long way,
and nettles, well-only a bit has to be left behind.
£150 sounds a lot of money to flail 1/2 acre.
We have an 'Allen scythe' type mower, might be worth investing in one? (there again - ride on sounds much more fun, and easier!)
How bad is it? ie-is there more weeds than grass?? have you a photo?
thought - Get some geese :-) they'll keep the grass short so you can deal with the weeds