Stacy, way to go on the exercise!
Rabbit's right - you need a minimum of 24 hours rest between working muscle groups so back-to-back full body workouts aren't a good idea.
You could do three full body workouts per week and double up on cardio on the off days, as an alternative. Many people start out with full body workouts and then graduate to splits.
Or - if you want to lift five days per week and don't want to do a traditional split - you could alternate upper and lower body days.
But most people who lift five times a week do a split, usually similar to this:
Monday: Back
Tuesday: Chest
Wednesday: Legs
Thursday: Shoulders
Friday: Arms (bi's and tri's)
with abs thrown in two or three times.
If you train each muscle group intensively, once a week is usually enough.
Like most things in the gym, there isn't any 'right' way to train, so do what works best for you (so long as you're not working the same muscles every day).