If it were me, I'd try more than one method to see what works best in your particular neck of the woods.
I have heard of putting down cardboard for weed suppression, then putting soil, compost, organic matter on top. This may be a variation on the lasagna method Sally mentioned.
Even if you mostly grow vegetables, you might like to have a few hardy easy-to-care-for perennials (or herbs or reseeding annuals) in self-watering containers for the pollinators and beneficials, and to get your "green growing things" fix. They could go in the ground next year?