I would almost never recommend using landscape fabric in garden beds! All of the hardest, thickest and worst patches of weeds I have ever dealt with have one thing in common. That one thing is landscape fabric. Mulch on top of the fabric breaks down and creates compost for weeds to grow into. They sprout on top and grow roots through the fabric so when you go to pull them, they almost never come out clean. Trust me, it is a huge pain in the.. Not only that, but you are installing a barrier that will prevent soil building and the natural mingling of micro and macro organisms in your soil and the mulch layer. Not good for your trees! Then you have big chunks of black fabric surfacing from below the mulch in a year or so and it looks terrible. You can probably tell by now, but I hate landscape fabric with a passion! =] I will use it under pathways, patios, french drains and other places where I'm not growing things.
What I would do if I were you is this:
Use a string trimmer or something to cut the weeds down low to the ground. If there are seeds present, try to cut them off and discard them first. I would only really worry about especially rampant weed seeds in this scenario. Leave the clippings there. Take some plain brown cardboard or news paper and lay it over the weeds. If you have compost, put some compost over the cardboard. If not, just put whatever mulch of your choice on top. To prevent weeds, just add more compost or mulch every year to suppress weed seeds from germinating. That's it. Cardboard does the same work as landscape fabric, but it decomposes in about 6 months to a year, making it a much better alternative. This is called "sheet mulching" It's an easy way to establish new garden space or deal with really tough weed patches.