JM - back to your original question. Teacup754 and needrain (Donald) are absolutely right in saying not to use rubber mulch. A lot of people use it but it has no benefit for the soil. With natural/organic mulches you'll probably find that they'll eventually break down and need to be refreshed. Cost and effort totally worth it. (speaking from experience)
About a month or so ago I was at a favorite local garden center. While waiting to check out I saw a product claiming to eliminate nut sedge. I had to hold back the urge to giggle.
Coincidentally, lately I've been taking pictures of the many and varied weeds in my yard. So far I've definitely identified one with the common name "Madder". Easy to remember as I get madder when I see it.
As I think others have said, when pulling weeds, thankless task as it is, go deep. Try to get the whole root. I've read that with some weeds it can be easier to use the "off with their heads" method. It prevents them from getting sunlight, oxygen, etc. So far it seems to work for me.
And do listen to Gramma Char about NEVER using Roundup.
I have a few more suggestions but someone is knocking at my door. (why people ignore my doorbell I just don't know)
