No, your dresser and night stands do not have to match.

Whether you paint the dresser or not would depend on the overall look you want for the room -- you might like an all-white room, or one that mixes soft coastal colours. A powdery blue-grey could look good (chalk paint?). I suggest you browse https://www.houzz.com/photos/bedroom/type--master/query/coastal/nqrw/p/36

for beautiful coastal colour palettes.

Your choice of bedding will depend on the same decision about overall look. You might consider something with texture to it.

If you really want to unleash Houzz's creative side, post a few pictures of the room as a whole. Let us know, for instance, if you are willing to paint the walls, are looking for window treatments, and any other ideas you might have.

Select your bedding FIRST. Then select a color to paint the dresser. Beds are layers......

Many authentic coastal cottages are vacation homes and are furnished with a mixture of styles and colors. Lots of tag sale/flea market finds, cast-off furniture from the primary residence, painted to make them look more cohesive or a mixture of painted and stained brown furniture. Use natural, organic materials like sea grass, woven bamboo/grass/wood shades, grasscloth. It's a casual look, with nothing precious or too serious.

There are a lot of ways you can go, here are some photos for inspiration: