Well, I would go with Benjamin Moore paint, if you paint. Good products. You get what you pay for.
The least labor intensive and best result I think would be to remove the top, buy and cut a new top out of MDF and apply new laminate, if you are comfortable installing laminate. It definitely is not something everyone wants to do themselves. I have done it and I like doing it. Most people don't.
If this cabinet has a top like a regular cabinet, then you can remove the top. It is probably stapled down before they put the laminate on it, and you can use a hammer to tap it up from underneath (take out the drawers if that is what is in the cabinet, or open the doors and hammer from underneath starting at one edge and work your way around carefully).
Laminate is not easy to do unless you have the right tools. You need a laminate router to finish the edges. It can be done with a file but it gets done faster and better with a laminate router. You need a laminate knife, which is cheap and available at most hardware stores where they sell the utility knives, usually. You can also cut it with a circular saw and a fine toothed blade. But to me that is overkill.
They have water based adhesives now. I prefer solvent based, but I also use a chemical respirator, and you don't need one with the water based adhesives.
On the painting choice, I personally don't feel that would look good. But if you want to do it, try that Benj. Moore paint that other person suggested, maybe it will look ok if you properly sand the surface first and re-glue the edges that are coming up. I would sand with a finer sand paper grit before finishing, a fine enough grit so that there are no sand swirls or sand stroke marks in the laminate. You may have to gradually increase the number of grit paper to get there, ending with maybe 400 grit. You also may have to use a couple of coats of primer. If you can mask off everything, you could use a spray primer that is sandable, and that has a high build character, like some of the automotive primers in a can you can find at a lot of stores. These are easy to sand and after 2-3 coats produce a very smooth finish.