First things first: there's actually a kind of "industry standard" for snare drums that works for almost all applications. The batter head is a single-ply, white-coated model, while a particularly thin, clear head is used as the resonant head. Most snares come equipped with this setup, and the majority of drummers play this combination.
The reason is simple. For a dynamic sound, a single-ply batter head is the best choice because it translates the player's nuances into the instrument effectively and delivers a transparent attack. The white coating provides a slight damping effect and helps control sustain. Additionally, it allows for playing with brushes, which require a slightly textured head for full tonal expression. Typical representatives of this type of head include the Remo Ambassador Coated, Evans UV1 Coated, or Aquarian Texture Coated.
The very thin resonant head captures the movement of the snare wires optimally, transforming it into the characteristic "snare" sound that gives the snare drum its name. You can identify this type of head by the names "Snare Side," "Snare Resonant," or "Hazy." Regular clear heads should not be used as snare resonant heads, as they result in a duller sound with less sensitivity.
Some manufacturers bundle both types of heads in a snare drumhead set or package. For upgrading your snare sound, this is a good deal because you can save a few bucks compared to buying them individually.
Many drummers swear by double-ply snare drum heads such as the Remo Emperor Coated, Evans G2 Coated, or Aquarian Performance II Coated. The advantage of the second layer is a more controlled, subjectively "fuller" sound and increased durability compared to single-ply counterparts.
If you like a lively snare sound but feel it could use a bit more attack, opting for a snare head with a center dot is a good choice. Manufacturers affix a round dot to the top or bottom of the head, reinforcing it. This adds a bit more punch and focus to the sound and prolongs the head's life. A classic example is the Remo CS (Controlled Sound), available also in a double-ply Emperor version. Evans calls this treatment "Power Center," and here too, you have various options to choose from.
Some drummers love them, others hate them. We're talking about overtones, also known as ringing or sustain. They occur at the edge of the head and can either add liveliness or be uncontrollable "whining," depending on your perspective and musical situation. However, they can easily be managed with appropriate dampening products or, do-it-yourself with gaff tape or tissues. If you prefer a ready-made solution, you can buy a pre-dampened snare head. A built-in dampening ring at the edge eliminates vibrations and delivers a controlled, dry sound. The Evans Genera Dry is a very popular model, and many drummers opt for the Remo Powerstroke 3. If you want a combination of attack, high durability, and a dry sound, products like the Remo Powerstroke 77 are recommended. They may be pricier, but heavy hitters in rock or metal genres will find themselves replacing snare heads less often.