Gwen, that's what the Dirtex is for. The old favorite for cleaning oils and greases was TSP. This is really good but it does get to your hands and it seems like the TSP/water invariably runs down your arms so even if you wear gloves, it still gets on your skin. Dirtex contains TSP but it is somehow made so it is not so tough on your skin. Something else that you might find on your wood is wax and the only way to really remove that is with naptha or a similar solvent. These are all flammable so you will want to read and strictly follow the directions on the can.
The last possible contaminent is silicone, which is in some furniture polishes. I don't know if it is in Liquid Gold or not. I do know that it is in Pledge furniture polish. Silicone will cause the primer and/or paint to "fish eye". "Fish Eye" is where the paint kind of balls up in moonlike, circular craters. The B-I-N sealer/primer is shellac based and this should handle silicone. Spraying shellac is better than brushing because the brushing can bring the silicone to the surface but you are probably limited to brushing. That's why you want to use 2 or 3 coats of the B-I-N. That still may not seal in all of it but it should cut it down considerably.