Fighting weeds can become a bit of an obsession. Remember, they aren't alien life forms - like nearly all plants they need leaves and light to thrive, they're just rather better at getting going in cold weather than most veg. And also, having a few around is unlikely to cause major damage to your crops, although it might hurt your self-esteem. I agree with the 'clear and defend' policy advocated by others. Get a patch reasonably clear and planted up with veg, keep the weeds down there and then move on to clear the next bit.
With brambles, try to get out the massive lump at the centre, and as many roots as come with it - usually they're in the place where several pink shoots come up in one place. I used a grubbing mattock for this when clearing my plot. The side roots will shoot, but if you keep taking the top off, or digging them out when they pop up, eventually you will get on top of them.
As you work the soil, the bindweed will eventually give up (it likes to be left alone). Couch grass will also give up if you keep taking the top off and as many roots out as you can grab. Once the top layer is loose, the weeds come up easier and you will hopefully pull up a bit of root each time you tackle them.
With the dandelions, dock etc my approach is generally to stop them seeding above all else, but even that can be futle if a neighbour doesn't do anything - the wind spreads the joy.