Calculating base resistors of a NPN driving a LED
You don't want 3.3V on the base of the transistor, because that would utterly destroy the BE junction, which behaves like a diode: its V/I graph rises very sharply at ~0.6V.

I'm not sure what you want R2 for, R1 can supply the base current to turn the transistor on. 

Let's assume 2V for the LED + T1, so 3V for R1. That gives 3/220 ~= 14 mA. Assume a modest B of 100, so you need 0.14 mA base current. Assuming 0.6V Vbe and no R2 that means R1 = (5-0.6)/0.14e-3 ~= 31k. If you want full saturation you can use a B of mabye 20, for an R1 of ~6k.