There are two critical elements that make for a great finish - selecting the right brush, and using the right technique. Practice counts as well. You don't expect to cut perfect dovetails the first time round, nor should you expect to achieve a perfect finish without practicing your finishing technique. I frequently choose brushing because I have a small shop and brush clean-up is fairly quick.
Most of my finishing is done with shellac or varnish. Occasionally I'll use a water-based finish for light-coloured woods when I want a super clear finish. However, I've never used lacquer, so my comments won't apply to this type of finish.
The most important part of a brush are its filaments (aka 'bristles' or 'hairs'). It’s the filaments, along with your brushing technique, that will have the greatest impact on the quality of your finish. With proper care brushes will last for years, so save yourself a lot of frustration by using quality brushes right from the start, and keeping the brushes in top condition. Cheap brushes will invariably result in cheap looking finishes.
The shape of the brush tip is also important. Avoid brushes that are trimmed flush across the end. A chisel tip will give you much better performance.
Basically, there are three kinds of filaments used in brushes - natural (usually hog bristle, ox hair, or badger hair), synthetic (made from polyester or nylon), and natural/synthetic blends. The general consensus is to choose natural brushes for shellac and varnish, and synthetic for water-based. However I've had good success using natural/synthetic brushes and synthetic brushes with shellac and varnish when I thin the finish by 10% to 20% with its solvent.
Natural brushes work well on shellac and varnish because they carry more finish (i.e. to 'load' the brush), than synthetic brushes, so that you can lay on more finish with each brush stroke, and maintain a wet edge as you work. When buying a natural brush, look for filaments that have flagged ends – a split at the end of each individual filament. The flagged ends enable the brush to hold more finish and release it with minimal brush marks.
There are two general types of natural brushes. The most common are made from the hair of hogs, typically referred to as 'bristle', or 'China bristle'. Any brush that's labelled 'bristle' is going to be made of hog hair. Hog hairs have naturally split ends. They also taper from the base to the tip, which makes the hair strong yet gives it a lot of spring, so that it maintains its shape in use.
Higher quality natural brushes are made from ox or badger hair, which is a softer, finer, and more pliable filament than ox bristle. You pay a premium for ox or badger brushes, but they do leave a finish that is as good as it gets.
With any natural brush you'll want to remove any dust or loose filaments before you first use the brush. Shake it out vigorously, then dip it about 1/2 of its length into the appropriate solvent for the finish you'll be using, and then gently tap it against the side of the container.
For water-based finishes use synthetic brushes, because the water in the finish will cause natural filaments to swell and lose their stiffness. Most synthetic brushes have polyester or nylon filaments, or some combination of the two. Neither are as absorbent as natural filaments, which means you have to load up the brush more frequently. Most manufacturers whip the filaments to split the ends into flagged ends to give a smoother finish.
For large surfaces use a 2" to 4" wide brush, while for smaller panels, frames, edge work, and legs, choose a narrower 1" to 1-1/2" brush. It's true that an angled (or 'sash') brush allows finer control in corners and tight spaces, but rather than adding yet another brush to my kit I simply switch to a narrower brush, which I find works just as well.
If you typically work with small items, then pick up a couple of small artist brushes (available with both natural and synthetic filaments). They excel at working in tight spaces, and the super fine filaments allow the finish to flow onto the work easily with virtually no visible marks.
When applying a finish think about scale. A large surface has the capacity to absorb finish at a faster rate than a smaller surface or narrow trim work. Using a heavier load on the larger surface makes it easier to maintain a wet edge. Conversely, applying too much finish to a carved or contoured piece will result in runs and sags that can be difficult to correct. With practice, and paying attention to the feel of the brush as you apply the finish, you'll learn to identify the correct load for each situation.
When loading the brush you only need to dip the bottom third or half of the brush into the finish, and then wait for the finish to wick into the brush. Before moving the brush to the project, adjust the amount of the load by lightly pressing the brush against the side of the container.
Rather than brushing from one end of a panel to the other end, begin by placing the brush a couple of inches from the end of the panel and move the brush to one end. After completing that stroke, return to the starting point and brush back to the opposite end. As you get to either end of the panel the brush should just glide off the top without moving down the edge of the panel. After completing the first pass, go back and use the tip of the brush to gently work the finish across the edge.
Brush cleaning doesn't have to be arduous or time consuming. If you're applying a finish over a day or two, then don't bother cleaning the brush. Instead, suspend it in a container of the solvent for the finish - just make sure the tip doesn't stand on the base of the container or it will curl up. Before using again, lightly press the excess solvent out of the brush on the side of the container.
To clean a brush used for varnish or water-based, you want to rinse the brush several times in the solvent for the finish you're using (mineral spirits for varnish, water for water-based). I do this three or four times, and then wash the brush several times with warm water and dish soap. For a varnish brush, rinse the brush first with a citrus-based cleaner and then again with water to remove the final traces of solvent from the brush.
Shake out any excess moisture by swinging it up and down several times, and then wrap the filaments with a piece of paper - I use strips from paper grocery bags. This allows the bristles to dry, and keeps dust from getting into the filaments.
My particular brush arsenal consists of two brushes for each type of finish. For shellac I use a 2" wide ox-hair and a 3/4" synthetic; for varnish, a 2" and a 1" bristle brush; and, for water-based finishes a 2" synthetic and a 3/4" synthetic. The type of woodworking you do will obviously affect your choice of brush.
Buy good brushes, practice applying the finishes you intend to use, take the time to clean the brushes after use, and you're three quarters of the way to a perfect finish. The last quarter comes from experience.