Each artist has their own unique preferences for what their instrument should sound like. Often, different sounding instruments are needed depending on the kind of music style they perform. Getting the right sound may become really involved as both the instrument and the amplification/effects chain plays part the end result. Personally, I am biased towards a clean, brilliant, sound with plenty of headroom as that produced by Alnico V-based, single-coil pickups.
Considering only the guitar, evidently, body acoustics and pickup design requires a fine balance; either can accentuate a range of tones, ranging from “warm” to “bright”. Quality, off-the-shelf Stratocasters often strike a wonderful balance to achieve that sought-after tone. When building your own, there is this quest for the perfect tone. It is not surprising then to hear of how much money folks will spend on pickups. In fact, there is quite an industry devoted to special pickups.
Basically, a single-coil magnetic pickup is simply a coil wound with thin insulated copper wire on a coil form. The top and bottom of the coil form is made of thin fibre plates with holes through which six rod magnets pass, one rod for each string. Vintage pickups has rod magnets of slightly-different lengths, specially chosen to produce and even balance across the strings. Such a coil has specific electrical properties: DC resistance, inductance, and capacitance (due to inter-winding capacitances). These properties, i.e., inductance and capacitance results in the coil producing a natural resonance peak (as per 2.pi.F = 1/sqrt(L.C)). Usually, under no-load conditions, that frequency is in the 8-10KHz range, that may sound somewhat on the treble side.
The shape of the pickup resonance peak is influenced by DC resistance also by other magnetic properties. However, pickups often are wired into circuits that affects resonance and shape of the peak. More than often, the resonance peak moves down to the 4-5KHz range. This frequency response of a pickup could be thought of as the "voice" of the pickup and is a big factor in what makes a certain pickup sound the way it does. This is where the art and science used by various pickup manufacturers comes in; how to engineer a pickup's electrical and magnetic properties, develop electronics to deal with impedance matching and tone shaping, i.e., the never-ending quest for "that" sound.
Here are a few a personal observations:
A tonal classification for various pickups (see the Table below), keep in mind the kind of body acoustics that the pickup is to be matched to. Don’t be misled by price; expensive, boutique pickups are hand-made works of art, so expect to pay accordingly. Beware, they may not sound any better than a cheap knockoff. Many cheap imports are actually quite good, usually reverse-engineered from the real thing. Rather, consider quality of workmanship, like for instance, potting and whether sufficient measures were taken for corrosion prevention (especially between windings and magnets), perhaps consider a nice-looking finish. It is OK to look for paper-based bobbins as those often allows closer proximity between wire and magnet, also promotes better potting. Often, plastic bobbins are not suitable. Except for shielded vs. plain, the type of unshielded hookup wire (Plastic/Teflon/Cloth) is of little importance, unless you are restoring a vintage instrument for its appearance. Be aware that pole spacing between pickup types sometimes differ, plastic covers are not always interchangeable for that reason.
Choosing a noise-canceling pickup is another story.
The table below is a summary of electrical/acoustical properties of a number of pickups as used on Stratocasters. These are single coil pickups, some that I have tried and tested on my guitars. Where indicated, measurements were taken with a HP4260A Universal Bridge. For magnetic field strength measurements, I use a simple home-made meter with a Hall-effect probe. Gauss meter.
The list is ordered by perceived brightness, (1) being the brightest, higher numbers being progressively "warmer" (bass).