A pet hate of mine is the free sponge applicators available with a high percentage of eyeshadow palettes. Not just for the obvious reason, it is difficult to do varied eye looks with a piece of foam, but also because sponge applicators (for face and eyes) harbour bacteria. Brushes can be cleaned as and when required, and depending on the quality, can last for years and years!
For someone new to eyeshadow brushes, I would recommend starting with three to get familiarized. A blending brush is essential when contouring the eye. Although there are flat tipped ones available, for a beginner I would go for a fluffier, denser brush. The second brush for starters would be a small flat eyeshadow brush for the application of eyeshadow to the eyelid. There are many to choose from, and most brushes you will find have a multitude of purposes. And finally, the most versatile brush of all three, an angled brush. This is flat and has an angled edge for doing more intricate and detailed make up art.
If your new to eyeshadow as well as brushes, it would be beneficial to buy a trio of eyeshadows or perhaps a quad as this takes the guess work out of what colours go with what. Not always but more often than not, the shades are varied tones of the same colour. For long lasting eye make up, I recommend priming your eye so the eyeshadow has a base to stick to. There are a whole array of eye primers available, but if this isn't something you can lay your hands on, a little concealer blended gently over the eyelid and brow bone should do the trick.
Taking the larger of the brushes, sweep the lightest of your eyeshadow shades over the eyelid and up to the brow. Its nice to use a shimmery colour for this to illuminate the brow bone. If you have tired eyes and want to give yourself a more wide eyed and refreshed look, take the light shimmery colour onto the smaller eyeshadow brush and apply around the tearduct area. Now the brush for eyeshadow contouring, just the general smaller eyeshadow brush. Taking a medium toned colour onto the brush, follow the natural crease of your eyelid. If the brush is fluffier, this can be done with small circles and "windshield wiper" motions which allows you to semi blend at the same time as applying. If it is a flat shadow brush then take the larger of the brush and blend upwards, adding more of the lighter colour to the brow bone area if neccessary.
Now taking the angle brush, take the deepest of your eyeshadow shades and using the flat angled edge trace the crease of your eyelid. Delicate blending is essentially when contouring in this way, so use the smaller eyeshadow brush for this and don't blend out towards your brow as before, just blend gently into the initial crease colour. This look could be complete, but for a smokier look take the darkest shadow onto the angle brush again and line beneath the lower lashes.
Add some mascara and liquid eyeliner if you desire and your all set. The best brush for eyeshadow contouring? All three play a part, but for a more cut and defined crease colour, I find the angle brush to be the most effective.