If it's textured you have to get in the grooves which you can't do with a cloth. Pour some dish soap on a nail brush or other soft or nylon bristled brush and scrub in a circular motion. Then rinse well
You can protect from stains with a coating of gel gloss wax

Once you get the formica clean, you can protect it and give it a sheen with a coating of car paste wax. Did that for years with my 1957- built- kitchen counters. Apply the wax, let it dry to a haze, then buff with a soft clean cloth.

The cleaning solution you use should have a degreaser in it. Use something like Fireball or Greased Lightening not the "ordinary" cleaners off of the grocery store shelves. Go to Home Depot or a hardware store. If your counter has texture use a soft scrub brush instead of a sponge/cloth.

Grease build up on plastics that is difficult to remove, is caused by frying. You may want to consider getting a filter fan.