The first 7-string electric guitar to appear in North America may have been the one that Epiphone custom-built for jazz artist George Van Eps in the late 1930s. Van Eps' own signature series was probably the first 7-string to be mass-produced, and since then it's enjoyed its own niche on the music scene alongside its more common 6-string counterparts. Of course, adding a seventh string to an electric guitar also means fitting the instrument with pickups so that can 'hear' it.
Just like those for more mainstream guitars, the pickups for a 7-string come in two major types: single-coil and double-coil. Single-coil pickups, icons on guitars like the Fender Stratocaster and vintage Gibson models, are classic parts that have been used widely since the very first electric guitars. Humbuckers, on the other hand, first appeared in the 1950s as a solution to the interference, or 'hum,' that affected single-coil pickups of that era. With modern design improvements mitigating background noise in any pickup, the biggest difference between the two today is their individual tonal characters. Single-coil pickups tend to have very good clarity and produce a sound that's bright and crisp, while humbuckers combine the signals from two coils to create a high-output tone that's heavy on bass.
Most pickups of either style are known as passive pickups. This means that they consist of just the magnetic coils and wiring, passing on a raw signal to be sent to your amplifier. If you want to modify your tone before it leaves the guitar, you'll need an active pickup. These include their own preamp, filters or EQ built in, which allows them to drive amps and gives them enough power to overcome long cable leads. An active pickup also helps to define the guitar's sound and reduces buzz and noise, all before the signal even gets to the amp.
Active or passive, double or single-coil, vintage-style or modern: these are all choices that are completely up to you. Pickups are a matter of personal preference, so there are no right or wrong options—it just depends on the genre you play and the specific sound that you want to create with your 7-string electric guitar. The best advice anyone can give you is to experiment and try a few different pickups… you'll know the right ones when you hear them.