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Yes, stock keys SHOULD get 1.5-2" no problem unless the torsion bars are worn out. I got 1.5" out of the tahoe with plenty more to go.
I mentioned the RCX kit (same thing I am looking at for the burban) Many lifts out there that claim 6-7" are really only 4.5-5" then cranked up anyway. What I am doing on the burban is a 6" kit with no crank to give me about 5" with great CV and ball joint angles.
RCX also makes a 3" lift that is keys (i think), new upper control arms to help correct the ball joint angles and an add a leaf I think. The CV angles would just scare me on that though.
A body lift is another option and can be done cleanly with gap guards, paint the wheel wells and paint the frame, add some side steps or running boards to hide some of the frame.
Biggest factor: How much do you want to spend and think long and hard about if you will want to go higher later. I have 8" of lit in the front of the tahoe and would love another 3+"