Richard, Kilz is a great product. I have used the oil based and it is kind of miserable to use. I have not tried their water based, but it should be a lot more user friendly. Let me offer another suggestion. B-I-N is an alcohol based stain blocker with shellac in it along with other things. It is user friendly and dries quick. Being alcohol based, you can get a mild high if you don't have some ventilation. It is available in a spray can, but the cost of doing a whole room would be excessive. With any of these products, follow the manufacturers safety precautions on the can.
Just to be sure that you understand, after you use Kilz or B-I-N, you will have to repaint. There is no product that will go under your paint to block a stain.