Roundup or you can burn them with a propane torch. I'd get the touch kit if I were you.

Spraying a weed killer or burning the visible plants may, temporarily, get rid of the top growth of those plants but will not do much about the roots that are under the bricks and soon there will be more top growth. The long term solution is to pull up the bricks, clean up the roots under them and then replace the bricks.

If you kill everything with boiling water, then refill the cracks with a new layer of sand, swept & packed into the cracks well, that should keep it clean for a reasonable amount of time.

Glyphosate (available as the generic weed killer) will kill the weeds, roots and all.

Then you can re-set the bricks. It takes regular maintenance to keep weeds out of paths.

The big clumpy grass - spray the clumps to kill them all.

AC,I also have a brick patio that gets a lot of grasses growing in it. I find that a lot of them pull out pretty easily. The really tenacious ones that won't budge can get spayed. It might look overwhelming now, but an hour or two of hand pulling would clean that entire area. When I pull the grass out ,the soil comes out with the roots,leaving more space in the cracks to fill in with sand, like Tiffany said.

I poured pickle juice on some weeds gowning in the cracks in my patio. The weeds looked rather sickly for several days before they began to recover.