There is a limit to how much you can save on airfare. Check the travel sites (airgorilla, expedia, priceline, travelocity, etc.) and also check the airline websites. I have often (not always, but often) found the best fares on the airline websites. Check with a real travel agent to ask about promotional fares and special deals.
Assuming you are from a country that participates in the Visa Waiver Program, go ahead and register. It's free, valid for two years (multiple trips), and you don't need your exact travel plans. Print the confirmation and keep it with your passport:
https://esta.cbp.dhs.gov/
http://travel.state.gov/visa/temp/withou…
http://www.cbp.gov/xp/cgov/travel/id_vis…
Travel agents sell trip insurance. It's cheap, and you can get coverage for medical treatment, trip cancellation, and lost baggage. Try to get medical insurance that pays the bill rather than reimbursing you after you pay.
Along with airfare, accommodations are usually the largest cost for a trip. The USA does not have as many youth hostels as Europe and the quality is irregular. An example of a good hostel where I live is:
http://www.indiahousehostel.com/
Consider joining SERVAS, which will give you local contacts in many places and you have the opportunity to stay with hosts for free:
http://joomla.servas.org/
Couchsurfer is reportedly similar but I have no personal experience with the program.
You might want to re-post your question in the Los Angeles section of the Travel section to get more answers from locals.
Good luck!