For those who are used to economy class travel in Australia, coach class (i.e. economy) in the US on a legacy carrier (AA, United, Delta, US Airways) or LCC (Spirit, Frontier, etc.) can be a bit of a shock. The planes are often very old, they're cramped, the amount of stuff people carry on is beyond a joke, the service is often poor, and you'll usually pay for baggage, meals, and anything else they can think of. In my opinion, they're to be avoided if possible.
On the other hand, airlines like Virgin America and JetBlue are very good, or at least of a similar standard to what you'd expect from Virgin Australia or Qantas domestically in Australia. If you're at all worried about space, JetBlue has a 34" seat pitch as standard, which is 2-3" more than others. They even have an Even More Space option which costs extra (from about $30 I think) depending on how long the flight is; that gives you 38" seat pitch. Virgin America have a Main Cabin Select option, which is a quasi premium economy. As well as providing more leg room, they also bundle in meals, entertainment and baggage, that you'd otherwise pay for separately. However, the extra cost for MCS is significantly more than the upgrade on JetBlue.
While Virgin America and JetBlue both have fairly limited route maps, they both fly from LAX and LAS to JFK, which is lucky for you.
I'd use something like ITA (matrix.itasoftware.com) or Expedia to look for and compare flights, but then would book directly with the airline's website. There shouldn't be much if any difference in price, and if there are any problems, you'll end up dealing directly with the airline, rather than having to go through a middleman.