Could you recommend a good weed killer?

If some of the weeds are brambles, or woody, there won't be an easy solution. If not, because you want to lay turf in the area, that precludes any strongly effective weedkillers because they leave a residue in the soil for some weeks/months.
The only solution in this situation is to use something like Roundup, sprayed on active growth (remember, you need the green growth for the weedkiller to work - you spray the leaves, it enters the sapstream and works back to the root and kills it). Woody weeds, like brambles, will need to be either dug out (deep roots!) or cut back and the main roots treated with brushwood killer, like SBK. (My blog on tree stumps will tell you how to use this, though I would add, if treated roots are under where you want to turf, you'll need to cover them with a pot or something, replace the soil and wait a while before turfing.)
I have to say, there's no real substitute for digging and removing the weeds by the roots - backbreaking, but quicker in the long run!