Making % based grids are incredibly easy, I think unless you're going to be using all the features of something like Bootstrap, you're just giving yourself a lot of extra bloat. Making a responsive grid system takes no more than 10/20mins and you'll have exactly what you need, nothing more, nothing less.
Here's a video about making a simple 2 column, % based grid.
And here's a blog post going through pretty much the same thing if you prefer to read about it.
To make mobile specific CSS you'll need some media queries going on, here's a post about that.
Also, if you're going to use media queries, don't forget to put:
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1">
in the head
of your pages.