Often times people think that merely having a good portfolio will get them in. There is a lot to graphic design beyond simply making compelling logos - you also have to make those logos printable at a cost effective rate.
Going to press is more than simply pressing "print", and you have to be able to appreciate that. A home printer has the benefit of printing relatively slowly, allowing for things like trap and registration to be less important.
You have to remember that you are competing against a lot of out of work graphic artists right now who hold college degrees or years of experience. Free software often times does not support the required features that will permit the adjustments to your work which are needed to make them printable. Even if I could recommend something relatively inexpensive, if you are unfamiliar with these techniques and requirements will limit your ability to become competitive.
I would recommend that you look into a local community college to start your career. After completing a two year program, consider getting a BFA in design, or even an MFA after that. I don't think these higher degrees are necessary, but they will help if you hope to someday be an art director at a prestigious firm. However, many graphic artists have far less education, if any at all. But i do think at this point in your career getting some college education in design and prepress is a good idea.
Still, a lot of people do learn this stuff on the job, and Inkscape and Gimp should provide you enough tools to get a portfolio out there. But i wouldn't hold your breath, getting a job in this field even after completing a college degree program is hard enough, getting a job with just a portfolio and no practical experience is going to be very difficult, especially in this market. Not impossible, but very difficult..
