Mand, to be honest, you'd be best arriving the night before the convention starts. I really don't recommend arriving on the day. By the time you clear customs (I've never got through LAX customs in anything less than an hour - last time I went, it took two hours) and baggage claim and then navigate LA traffic, you probably won't get to the convention hotel until about 3:30pm at the very earliest, and by that point, you'll have been awake for about 24 hours.
It's much better to arrive the day before, and have a relatively leisurely afternoon chilling out in your room and getting to know the local area, and then you'll feel much better the next day.
If you really want to book flights now, then avoid charter flights at all cost and go with one of the major airlines, like Virgin, BA or American Airlines. I thoroughly recommend flying Virgin - I always try to fly to the States with them.
The other option is keeping an eye on newspapers like the Daily Mail, because they sporadically run token offers for discounted flights.