Sorry to start a new post, but until the reply problem gets fixed, this is the only way we have to communicate!

I use old hay for mulch--old as in last year's hay. Old straw would work well, too. I've never had much problem with weeds, and here in Texas we have one of every weed invented. Hay/straw wouldn't interfere with your drip irrigation system, and at the end of the year you can just till in whatever remains. It does break down a bit over the season, especially in paths where it gets walked on.

From your picture it looks like you have a great garden spot. Let us know how the season goes for you!