The two books I recommend to anyone beginning with Photoshop are Scott Kelby's "Photoshop [any version] for Digital Photographers" followed by "Photoshop Classic Effects". You can follow up with video tutorials and other books, but these two will give you a thorough grounding in the basics, painlessly and fast. You need the photography title because that is the heart and soul of Photoshop, no matter what else you do with it, and if you're designing you'll be retouching and/or recoloring assets frequently.
Why these two books in particular? They are the most approachable I have ever found for a beginner, they're thoroughly practical, and Kelby's slightly wacky sense of humor means they're never dry. Both are entirely task-oriented; each chapter addresses a particular need or typical professional challenge and takes you straight into a well-illustrated step-by-step of how to get the product. No chapter assumes you've read any other chapter, so you're never swimming about wondering what he's talking about, never out of your depth, no matter where you jump in.
Unlike 98.5% of other books (and video courses) out there, Kelby does NOT bore the reader with a long introductory chapter on the UI. You learn the UI naturally and automatically as you follow along, using the same assets as are in the examples.
With those under your belt you will find you already have quite an arsenal of techniques at your fingertips (and the structure of the books means it's very easy to refer back to a particular technique if you don't recall the details). Deke McLelland's "Photoshop [version] One-on-One" is an excellent follow-up that also works for reference afterwards.
The National Association of Photoshop Professionals (NAPP) is a good $99 investment for a year. The site is packed with video- and text-based tutorials from some very clever people, at every level from beginner to quite advanced. I still keep my membership up to date.
If you plan to become a designer, don't neglect design as a subject of study unto itself. It's a common fallacy that knowing how to use the tools means you are now a designer. It is a fallacy, as thousands of painfully amateur flyers, posters and websites have proven ever since Microsoft Publisher and FrontPage arrived on the scene. (There is a special place in hell reserved for whoever dreamed up WordArt.)
Have fun, and good luck with your studies.