One big bonus with first class is that it's going to be less crowded. Second class is often standing room only, especially at peak times, and even if you have a seat the journey may not feel very comfortable with people standing all around you and half sitting on your lap. If the difference is only 60 dollars I'd say "Go for it".

As for seeming out of place... I don't think so. People travel first class for all sorts of reasons, not just because they're rich. I had a first class pass for a few months as a student when I working for British Rail over the summer - I was 22 at the time and very much looking the scruffy student. And you will probably see quite a few backpackers in first class - people who are just slightly too old to qualify for the youth pass but plenty young enough to travel with a backpack on their backs.