These filters do different jobs:

• UV filter: On most digital cameras, a UV filter usually has little or no visible effect on image color because the sensor already blocks UV well. Many photographers use one mainly as front-element protection, though any extra glass can potentially reduce image quality or add flare.
• CPL (circular polarizer): This is the most creatively useful of the three. It reduces reflections and glare on non-metallic surfaces like water, glass, and foliage, and can darken blue skies or increase color saturation. Your TV-screen test shows the same polarization effect. It’s mainly useful outdoors in strong light.
• FLD filter: This is a color-correction filter intended for fluorescent lighting. It compensates for the color cast that some fluorescent lights produce. On a digital camera, white balance usually replaces the need for this filter, so it often just adds an unwanted tint unless you specifically need that correction.

So yes, a CPL can definitely help you make stronger-looking photos, especially landscapes and scenes with reflections. UV and FLD filters are generally less important on digital cameras.