As a student, I felt the best way to get travel experience was by studying abroad. My college offered some great programs and I ended up studying abroad in Italy for a semester. That opportunity spurred my interest in travel and allowed me to visit multiple countries. I love reading Rick Steve's page to get travel ideas and even mock itineraries. If going abroad for travel right now seems unachievable, start small and start traveling to nearby cities/states.
Mexico is close and cheap. Highly recommended! I personally studied abroad in Brazil and it was a great choice. Also very cheap and a totally different culture. Google "study abroad programs in _____" and fill in whatever country you're interested in. Get out there Julia, the world is waiting.