I think the bigger question is; what are you going to be using the final design for? Will it be for...
Printing?
Plotting?
Both?
Second question is, what is going to be the primary use of the program?
Create from scratch?
Clean up provided artwork?
From the question it sounds like you are going to be creating designs from scratch.
Let me give a breakdown on the top 3 pieces of software:
Corel: Great for creating vector graphics. Great for converting supplied graphics into vector.
Illustrator: Great for creating vector graphics. Okay for converting supplied graphics into vector. Great at doing ad-slicks.
Photoshop: Great at manipulatiing photos. Cannot convert anything into a vector (however it can open a vector based file). Great for designing vehicle wraps.
My personal recomendation is to learn all 3 programs. It's "expansive", but as stated earlier in this thread, each program does something very well that the others either cannot do or just do poorly.
Corel tends to have super tiny file sizes regardless of the actual design size (I have always loved .cdr files because of that). Both of the Adobe programs tend to save HUGE files.