Photoshop is a must if you want to expand your skills. We use it more than Illustrator anymore. Then Illustrator.
Everybody says Corel and I suppose if you never plan to expand beyond the confines of the sign industry Corel is a good tool to know, but if you want to be able to work with outside designers and agencies, learn the Adobe suite, it's the standard of the graphics industry. 80% of our clients are designers or agencies and I don't think in 7 years I've ever had someone hand me a Corel file. We get .psd, .eps, .ai, .indd and .pdf files day in and day out and knowing how to work with those is essential.
Photoshop is an incredibly powerful design program if you understand how to use it as such. It's not just for cropping raster images. Once you really get the hang of it you'll find it as intuitive to use as a vector program, if not more so. I personalyl hate page layout programs like quark or indesign, but knowledge of them is critical if you want to be well rounded, they aren't really like a vector or raster based program, so if nothing else, understanding how they work might save you from some major headaches down the road if you ever have a customer that gives you one.
If you learn well from books, the "Classroom in a Book" series is excellent and really explains how things work. There are alot of tutorial sites on the internet as well, some with video, that really walk you through the programs. Don't get frustrated, especially with Photoshop, the amount of things that program can do is staggering, the learning curve is steep and there is alot to know and understand to get good results.