Advice on painting fake wood dressers?

I’ve had these dressers since I was a kid. They are the kind from Sears that are particle board (I think) with that “fake wood” sort of finish on top. It sort of looks like this. I want to paint them a very dark chocolate brown and add some stainless steel knobs. Currently the dressers are an ugly dark blue with beige tops and knobs.

I went to Home Depot and asked what paint I should use. I was given BEHR Deep Base, 100% Acrylic Latex in “Interior Eggshell Enamel”. Then they tinted it for me in the colour I picked. I also bought a 4” foam roller, masking tape, and those sticks to stir paint. I already know I have to sandpaper. However, do I need a primer? They didn’t say I did so I don’t think so. Should I do it outside? I’m worried because I have heard that this type of thin layer of fake wood can react badly to wet paint (bubbling and stretching). As long as I sandpaper thoroughly will it be okay? Do I need to use some sort of paint thinner on it before I sand it? What should I use to clean it before sandpapering? Any other tips and warnings would be appreciated. I am not knowledgeable in this field whatsoever.