I like this better, too! If there is any way to work a sentence about your mother into the first few sentences, that would be even better, I think. Because, although it's unusual enough that you're traveling the world in a year, it makes it even more unusual if you can work an evil mother into the mix

I'm thinking something along the lines of,"everything I'd been dreaming of for years--ever since I knew about dreams. When my mother kicked me out at age fourteen, she only made me work harder to achieve it."
That morning I had gone went to the credit union as soon as it opened. I withdrew exactly $2,790 in cash. Then I put the envelopes (so much cash required two envelopes) in my backpack and boarded the bus to head across town to my travel agent. It was the beginning of everything, everything I’d been planning for months, everything I’d been dreaming of for years. [Personally, I'd put an em-dash here instead of a period.] Ever since I knew about dreams. I looked out the window. [period or semicolon] I’d never seen sunlight so sparkly; [semicolon] the sky was a blue that you just wanted to swim in. I left the travel agent’s home office that day with a book of tickets: Denver to Los Angeles to Tokyo to Auckland to Sydney to Bangkok to Delhi to Istanbul, then I would train to Bucharest, where I would pick up my flight path to Cairo to Accra to London to Barbuda, Antigua in the Caribbean to Lima (via Miami) and finally back to Colorado, one year later. I had jobs and volunteer gigs set up along the way and had meticulously planned my budget to stay within the total of $8,100 I had saved. I’d even created mini guidebooks for each destination based on my research, completed for my senior project to graduate high school, with phrasebooks for each new language I would encounter.