When I straighten my hair, here's what I use for it to be silky soft and stay put:
First, I mist my hair with Bumble & Bumble Styling Spray. It's made to use before you blowdry/straighten your hair and protect it.
Next, I straighten in layers.
Then I finally add in some Bumble & Bumble Defrizz. It's a silicone based serum that locks hair in place while keeping it shiny and smooth.
This really works and my hair is straight even a day later! I tried many serums, sprays, etc. and I found that if it was just a tad humid, my hair would go crazy but not with this stuff!