ANY .... exposure to GIS is a good thing! It will do you no harm, especially in alignment/combination with your chosen acedemic background. GIS & an area of expertise -- a killer combination!
You can get a free trial download of ArcView by ESRI HERE (suggested by Mark Ireland). As Artwork21 said, this is the Microsoft of the GIS World. Underdark also has some strong suggestions. Open Source GIS development could prove both interesting & lucritive as well. I think it's fair to say that such skills will be in high demand when you finish your schooling. Personally, I would focus on ESRI as a starting point, and take it from there (that's just me - others may suggest otherwise). Perhaps you'll want to look at the Open Source side after getting your feet wet.
You can get a basic intro to the concepts HERE. If you look at the pane to the left, there are all sorts of resources at those links too. I would start with some reading to get an idea what GIS is all about, then try some of the exercises once you have a feel for things. Hold off on downloading the software until you're ready to start some actual exercises. When the trial runs out, check out other free software packages like Quantum GIS.
This is a way for you to get a feel (even if it's just to see if you enjoy GIS) without spending a penny.