I use Corel Draw. A very versatile , vector application.
One thing I like about it is that I find the pen and shape tools are easier to handle than PS's. No offense, guys.... that's just me...
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Judging from what you say the company does, you need to acquaint yourself with at least 3 of its core components - Draw , Paint and Trace. To give a nutshell run-through ....
Draw - This is the Main application for vector drawings and creating layouts for just about anything printed. Almost all my logo, brochure and magazine layout designs are done in Corel Draw. It features the use of layers much like what we have in PS. You can import jpg and even layered psds into your page layout and can convert them to bitmap. You can export CDR works into Photoshop. Bit-mapped images can be exported to...
Trace - As the name implies, the application traces your images creating a vector version. Depending on the settings you apply, you can get a rough or 95% accurate vector trace of any image. Imported back to Draw, you can edit this vector copy even further. I must warn you tho - that's a whole lot of nodes anchor points and shapes to work with most especially if you select full accuracy trace.
Paint - This would be the Corel version of Photoshop. Not as versatile as the forum's favorite weapon but it does almost what PS can do. Draw and Paint has filters that are familiar to you in Photoshop. More like water-downed versions.
In the event you are called upon to do Web designs, there's Corel Website Creator which is part of the 8 program Suite. I've launched it once before but I haven't really delved into it so there's nothing much I can say at this point.... lol .
This workhorse can be a bit RAM intensive most especially if creating complex images or multi paged magazines layouts with amounts of images. But for practicing, I'm sure your cpu can take it.
I do hope you get the job. Good Luck.
If you need help on CDR, give a holler.