Some lift kits support 37's - contact the manufacturer for recommendations and maximums - it also depends on your existing suspension. A 6" lift gives you UP to 6" of lift - if for example your rear leafs are already pretty flat and you don't add a leaf (and sometimes even if you do) your lift could only bring you up say 4 or 5" with a proper rake in the end.
Negative offset is the extent of how far the rim will stick outside the edge of the body. I have a -12 rim right now and I stick out about 1-1/2" from the body. Depends on the rim but the greater the (-) the more you will hang out. Don't jack yourself too high up without coming out at least a bit (in my opinion) the truck will start to look off balance and handle poorly with a real high center of gravity. Heavier offsets give a more 'planted' feel to the way the truck handles.