What are some good choices to use as a mulch over vegetable garden beds. Keep in mind, I have 9 4x50ft beds to cover so cheap or free would be helpful.

I'm trying to lessen my weeding and hold in more moisture. I'm battling what might be nutsedge 😂 too. I just can't keep up! I've got three young kids to manage with this garden too. I should also mention that my husband is highly allergic to straw so if I use it, I'll lose his help with weeding and harvesting.

Please Help! I spent 4 hours fighting a badly weedy bed today. It's exhausting and so frustrating especially since I don't think i irradicated most of it.

If you are battling nutsedge... bear in mind that mulch will not prevent.
But, will help keep the soil loose enough to make hoeing a reasonable option.

Check this thread:
The thread "Tree-trimmer, ROW Clearing wood chips for mulching????" in Vegetables and Fruit forum

I've been using our grass clippings as mulch. Normally we don't bag when we mow but every so often I do so I can use it as mulch (has to have been enough time since anything was put on the grass though). I also like using leaves from fall as mulch.

A summer mulch for my raised beds is pine straw. It is plentiful in this area and free. I use it to retain moisture and the moist soil makes weeds and be grass easier to remove.

You don't need to choose just 1 substance. If you can use a variety, it will add more benefit to the soil more quickly. Any organic matter that reasonably doesn't have seeds in it can be added to the "mulch." Do people bag leaves where you are? You can use any organic matter that is easily composted, such as leaves, shredded wood, kitchen scraps - especially coffee grounds, small trimmings from shrubs or trees, shredded paper, sawdust, whatever is available. Sometimes tree trimming companies love to have somewhere to dump a load of wood chips. You could call around and ask. The things I avoid using in compost & as mulch are bigger pieces of wood, thorns, meat & bones, anything salty.