How to click and drag select objects?

I don't have any experience with Illustrator and am trying to modify a file. There are a bunch of text objects (something like two dozen) and I simply want to select all of them without shift-clicking every single one. However, when I choose the selection tool and then click and drag to try to select the object, the background gets selected and starts moving with the mouse.

If I click outside of the layers and drag into them then I can select stuff, but it gets borders on the edges that I don't want to select.