Straw mulch

I usually grow very dense and use living mulch. I really like this method. One of the down falls is It's very bare in the beginning of each season. This isn't a deal breaker because it's not as hot in early spring, and in fall which is my second growing season there's still lots of plants covering the soil.
So why am I trying straw mulch this year? A few reasons, one is I haven't tried it, and I'm always looking to improve my garden.  The main reason is most of my garden beds are hugel beet. This is an amazing way to grow, and for me there's only one negative. My beds sink several inches each year. I don't know how much I spent on soil this year, but it was way too much. I had some of my own homemade compost, and if the bed is very low I will steal soil from the chicken yard. I don't know if it's realistic to think I can make enough soil, and or compost to keep my beds topped off.  
I decided to try straw. It's cheap, it keeps the soil cooler, keeps the moisture longer, and  I'm hoping it will decompose in place reducing the need for so much soil. ( the straw I got is wheat straw. I did seed seed heads, so I may get wheat. That's fine, I will just chop and drop it)
I bought the straw, tested it by growing beans. The beans grew and looked normal. There it sat. Last year I did this, and never used it. This year I was determined to use it. I put it around my veggies the other day. I have to say I hate the way it looks. I definitely waited to long, because the plants are abundant and pretty big, so I had a difficult time getting it into place. I did try to chop it up, but my chipper would just clog, and all the other ways I saw to chop it was just to much trouble. It's done now, so I hope I get good results. Of course after I did this I watched a video where paul was saying hay is a better option because each time you water it's like fertilizing. Oh well there's always next year.
I did try shredded cardboard as mulch last year, and I really liked it. It does break down very fast. I do have a lot of shredded cardboard, but not enough for all my beds.
What do you use to mulch your veggie garden?

I use straw mulch around my fruit trees and it does a really good job at suppressing weeds without me having to think about it. The main thing I noticed is you want it thick, like 10cm minimum, otherwise weeds just push through and you end up worse off because now they have a nice moist layer to root into. Slug pressure went up a bit the first year but once the birds figured out they could find them under there it balanced out. Curious how it works on your hugel beds since those already hold moisture so well.