What weedkiller to use?!!!

Weedkillers in your garden centre will have indications as to how long it takes for them to become inactive, which would be when you could begin planting.

Alternatively, I've seen land covered in black plastic sheeting, to exclude light and water. A few weeks like this kills most weeds, or at least weakens them enough to fork out.

I have used the black plastic method VERY successfully, several times. Black plastic leaf bags are economical. The key is to lay the plastic and seal the edges with wood strips (any old board or shelf will do!). The black stores heat, the boards hold the heat in. Kills weeds, grass and most any pest foolish enough to stay under the plastic..... Result is somewhat sterilized soil. Best done in full sun areas, but works anywhere. Be ready to use a hoe and rake deeply to remove debris, but it comes out easily. Your soil will be loose at that point and ready to add compost. If you are finding deeper live roots, just replace the plastic and wait another week. Educating the neighbors that this is temporary is also a good idea...... Good Luck!