I want to get a job at a print store such as Sir Speedy doing graphic design. What should I concentrate on learning most, Adobe Photoshop or Adobe Illustrator? I've heard that Photoshop is used often but I thought that maybe in terms of logos and such, a vector program like Illustrator might be more useful. Anyway, I just wasn't sure what I should concentrate on learning first.

They are used for totally different purposes. Photoshop is for photo editing. Illustrator is for illustrating/drawing. It's no big deal to learn the both well enough for your target job. If I had to guess, I'd say Illustrator, but go to the bookstore (just kidding, look online) for short tutorials on both. Better yet, go to Lynda.com and get some nice video tutorials. If you want to go deeper into one, then do so, but they have different goals.

I would ask the manager at the shop you are interested in working at. That way you'll know you're learning the most important program for the job, and you'll have created an impression as someone with a real interest in working there.
- I'm guessing Illustrator will win since it is much more focused on the printed form.

I'm self-taught on Photoshop, but have found Illustrator less intuitive even though there is some similarity between programs, there are also important differences.

I picked a book for Illustrator after reading through several and am very impressed with it. It's called: Real World Adobe Illustrator CS2, by Mordy Golding. There's one for Photoshop that looked equally good.