Don't take this as a flame, I'm just curious:
If you have been in training for the last 2 months, what the hell have you been doing if not hitting the gym and doing stairs/cardio?
I boxed for 7 years starting at 15 years old, and there is no other training boxers do besides cardio, gym type training, speed, and heavy bag, and sparring.
I mean you could be watching video tapes on other boxers but I'm guessing this isn't the case since you don't know what kind of training to do as a boxer.
Here is my opinion and advice:
Do as much cardio as you can, if you've never boxed your going to be very suprised at how fast boxing drains you. You main punching power comes from your tri's. Do lots of dips and tri extensions (rope pully works great).
You still need to work you bi's an chest and shoulders for the obvious reasons, but your tri's provide the majority of the punching power.
Again if you've never boxed before your going to learn really fast that you want your abs as strong as possible. Body blows will take out a new (unknowing) boxer really fast if his abs are out of shape.
Run your ass off, run like forest gump, then run some more.
Last but not least, I don't know if you have a trainer, I'm guessing that you don't based on this thread, but if you don't have a trainer get one. If you do have a trainer, get a different one.
Blast me an email if you want and I'll send you some of my old workout routines when I was boxing for the Navy, but bear in mind, if you not in shape you are going to die, you need to work your way into the routines, don't start off running 5 miles a day 5 days a week.
Jdabs