I grow my vegetables in containers and raised beds. It's much easier to control the soil and fewer weed seeds make their way into a raised bed. I do get some weeds in my big pots but it's so much easier to pull them out when they are up at a convenient height. Of course if you want a big garden, container gardening probably isn't practical but it is surprising how much produce you can get from a small space.
Here I have used an opened-up cardboard box to mulch near a tomato plant. The hose water uncovered some of it but I can quickly shovel a bit of dirt over it again. You can use lots of things as mulch. It just has to keep out the light. Old clothes, old reusable shopping bags, even opaque plastic if you punch a few holes in it are all possibilities.
I also don't stress if I have some weeds in the vegetable garden. Unless they are really out of control, the vegetables still grow just fine.
Here is a messy little patch that has been planted with nasturtiums and rudbeckia. In a couple of weeks, I'll know where the nasturtiums have sprouted and the rudbeckia will be bigger. I'll mulch around the plants with newspaper covered in dirt and I'll be set for the summer.
I hope some of these tips help you to enjoy your garden more. And remember , it's a garden, not a living room. A few weeds are not the end of the world.