The tendency for beginning trumpet players is to get a choked tone, especially in the upper range. Trumpet playing, range and everything included is all based on proper lip control, not pressure of mouthpiece between lip. I found that if you can play petal tones with control and finese (yes it is an idiosyncracy), playing in the upper range will get easier if you can master the low range. Also, working on low range long tones will give you a darker tone in the middle range.
As for the Arban's method, it is an all-inclusive tutorial to trumpet. Take every book there is and put it together and you have Arbans. Don't skip around though. Work from page 1 until you get to the Characteristic studies. Master that book and you're set.
There is no set method to playing, everyone has a different mouth. However, the concepts are the same. Take my advice as you will.