With such heavy weed pressure, I would recommend planting under landscape fabric, at least for the first year. Measure the fabric to size, and cut holes through the fabric at your planned spacing (an "X" cut would work best). If the soil is soft, just push the cloves through the holes; you can also use a bulb planter to make the process easier. Covering the fabric with straw after planting will provide additional weed control, help to hold down the fabric, and help to keep the soil cool next season.

IME the landscape fabric does not do much except wind up torn up in the soil, and the plastic (versus fabric) warms the soil too much. Maybe there are more resilient versions, idk.

The cheap 'landscape fabric' from hardware stores is, in my experience, fairly useless....but if you are willing to spend a little extra, look for getoextile fabrics. The polypropylene material works fantastic for weed suppression, while still allowing ample moisture to pass through.