Susan, I use Dirtex for most heavy duty cleaning and am real happy with it. The strongest overall cleaner is TSP, trisodium phosphate, and Dirtex is similar but buffered so it doesn't tear your hands up like TSP. If you are worried about the chemical name, your laundry detergent and canadian bacon and many other food products have it in them, probably. Follow the package directions on the Dirtex.
If you have new latex paint spills, putting vinegar on a paper towel and leaving that on the spill for the vinegar to work on the paint works great. For old and unknown paints, something like Goof Off will normally work.
There are a lot of similar products out there in both categories. They probably will work as well. There are small differences in ingredient lists and larger differences in price and advertising/marketing between many of these products. One thing that you will want to do is to follow the label directions exactly.