Each type of varnish has a different composition and different flow characteristics, so unfortunately there's no one brush that is the ‘best’. This is also reinforced by each user’s brushing technique.
Traditional marine varnishes, such as spar varnishes, are the most commonly used varnishes on boats and in the marine trade, as they are air-dry products with good UV resistance and predictable flow characteristics. They are solvent based and generally do not do as well with nylon or poly bristle brushes. After hundreds of years of experience, it has been generally accepted that natural bristle brushes give the most satisfaction, longest life, and most controlled flow. Depending on the specific application, there are different shapes, brush thicknesses, tapered brushes, and different natural bristle materials used. But is it really worth spending $25, $40, or more for a brush? The more expensive natural bristle brushes are made of better raw materials for extended brush life. These premium quality brushes are designed for different users and their preferred flow and brush feel/balance.
Two-part urethane varnishes have a stronger solvent content that may have a tendency to destroy synthetic bristle brushes, making natural bristle brushes a smarter choice for application.
Water-based varnish products and wood finish products should be used with nylon or poly tapered bristle brushes, because natural bristle brushes can swell up and permanently lose their tamed shape. The synthetic material does not absorb the water from the product, and the tapered bristles will provide the best control and release from the brush.
The topic of using foam brushes for any, or all of the varnish products mentioned above is always up for debate. Foam brushes generally release a controlled amount of material, they're cheap, disposable, and readily available. But when it comes to achieving a professional finish, a foam brush is not really the tool to use. Foam brushes tend to drag, as opposed to having a sense of ‘flow’ or feel, and it may be hard to manage applying too much or not enough material. Two-part urethanes will destroy a cheap foam brush in a matter of minutes, and will typically make the nicer foam brushes swell up and fall apart. Two-part products have a completely different sense of flow, and with foam brushes, they don’t take as well to ‘brushing’, instead letting the material sort of fall off the brush at the rate it wants to. When applying water-based varnish products, foam brushes have a tendency to drag the product around, and, similar to two-part varnishes, it's hard to really ‘brush’ water-based products with a foam brush. When using a foam brush with water-based varnishes, you may find that you're letting the varnish fall off the brush rather than ‘brushing’, and that you're just trying to control where the product flows.