You can test paint using Diggers Methylated Spirits. Get a clean rag and put some metho on the edge of the rag. Rub it against a section of the paint. If the paint comes off, it is water-based paint. If it doesn't come off and just becomes very shiny, it's an oil-based paint.
Once you identify which kind of paint has been previously used, you can now pick a colour and repaint over it. - EricL