There's a study that suggests 62 to 90 percent of a first impression is based on color alone. It influences the mood and perception of that initial interaction, but also has a psychological effect over time.
This is important to consider when selecting wood stain.
It'll enhance the wood's color, shape its appearance, and quite possibly affect the mood of those around it. Both now and in the future.
Deciding on the best wood stain can be complex, but let's boil it down to just three things to look at, so that you can go out and choose what’s right for your project.

Choose A Stain Based On Surroundings

Yes, before considering what you're staining or the type of stain you're using, try looking at the wood around it, if there is any. Then, find the undertone. 
Colors have a mass tone, which is the color you directly see, and an undertone, which shifts the color's look and makes it unique. 
Think of it like this:
There's brown. And there's sandy brown with lighter tones. And then there's burnt brown with darker red tones. And then there's muted brown with gray tones. The list goes on.
This is one way that interior designers and painters make an aesthetic flow from room to room. They find the undertone and carry it throughout. You can do the same by carefully choosing wood stain. By matching wood stain color throughout, there's a feeling of cohesion in the space.
The light that hits the stained wood will also affect its appearance, which will determine the texture of stain, be it matte, satin, or otherwise.
Whether the color is matched or customized, the type of wood will affect things quite a bit.

The Stain Should Complement The Wood

There are different types of wood and because of that there are differences in how they grow, how they appear, and how they're structured.
The texture of wood is relative to its species. Some species have smaller, closely spaced cells that cause a denser structure, affecting the absorption of stain. Other species have a coarse texture with large cells. 
For example, oak, ash, and chestnut have large pores that soak up stain quickly and can therefore be used with more types and colors of wood stain.
Birch and maple, however, have a stronger density and will absorb stain unevenly, causing many to avoid using dark colored stains with them out of fear that it'll turn out blotchy. 
A wood species like cherry has small pores that make it difficult to absorb stain, therefore making it harder to change its color. 
By thinking long and hard about the wood and its respective species, you'll find the right stain for the job.

The Type Of Stain Matters

Stain comes in different form factors. They'll generally include a dye or pigment.
Dyes are soluble in water and solvents. The particle size in dye is much finer than pigment. Pigment is generally insoluble in water and most solvents. Pigment is suspended in solvent, often referred to as a vehicle.
Dyes require a physical or chemical reaction, while pigments need a binding or dispersion agent. 
A pigment stain will have a tough time with finely grained woods, but dye stains will seep into those small pores.
Oil stains, often billed as "petroleum distillate," can contain pigment, pigment and dye, or just dye. Linseed oil in them gives the user ample time to remove excess stain before it dries.
Varnish stains can be left to dry without wiping. However, when excess stain is applied, there's less time to wipe it off before drying, which could result in the appearance of brush strokes in the final product. 
Water-based stains are less polluting and are easier to clean up but could raise the grain. They're quick to dry but will require more maintenance than an oil-based stain.
A gel stain, often oil-based with the consistency of pudding, is good for jobs that could end up blotchy, like with pine. It's applied to a surface in multiple layers like painting. Because of the layered application, it's a more forgiving stain.
Lacquer stains are fast-drying, useful for those who want to shorten the time between staining and finishing. 
UV light can be tricky with stains, causing them to fade over time, which is why metalized dye stain was developed in the 1950s. It doesn't raise grain and can be sprayed on relatively quickly with a fairly swift drying period.
The choice of wood stain will depend on personal preference, but will be heavily influenced by the wood itself and its structural characteristics.