I'm new to figs, but experienced in general gardening, so take my advice with that in mind.
You should know what the weeds are that you want to remove before attacking them. Some weeds will spread and become worse if you try to rototill them, and should be dug up instead.
I'd be inclined to start fig cuttings in containers, at least for the first year, which gives you a lot of control, and they won't be competing with the weeds. The potted cuttings can be sunk in the ground in spring, and grown that way to start them..
As for the weedy garden, if the weeds aren't aggressive, or an invasive species, turning it all over and amending the soil in the fall would be a good idea, imho. Depending on how large the garden is, once prepared, you might consider covering it with black plastic, weighted down, and well perforated to let rain through. Remove the plastic in the spring, and go from there.
I hope this helps--good luck!