Pickups:
When it comes to pickups, the choices are vast. The first thing to consider is the space they have to fit in, and the second is what is the difference in sound that you seek?
Although I can alter the wood to accommodate different pickups, you will very likely find something suitable that is made for the space you have. Just as you can get humbuckers that fit in the same place you had a single coil, you can find single coils to replace humbuckers.
The first pickup ever made was a single coil, and the main reason humbuckers came into existence was to reduce noise, as the name implies, by adding an opposing coil that is wound the other way around, and with the magnets upside down, AKA "Reverse wound reverse polarity" (RWRP). As a musician you may not need to know all of the electronic stuff going on there, but rather what it does to sound.
Humbuckers are loved by many for their noise canceling, but at a loss of tonal range, where single coils are loved for their dynamics, and hated for the noise. Thanks to the more recent trend to improve pickups, you can get noiseless single coils with all of the color and guts of traditional ones, and the difference in price is more than reasonable for what you get, so I highly recommend some Lace "Sensors" or Kinman single coils, the latter have to be ordered to fit the radius of the fingerboard, and are more expensive, but also the best sounding pickups you can get at the time I wrote this (it just turned 2015 a few days ago).
Basic pickup wiring:
The way pickups are wired can make a big differences in sound, and as long as you have more than just one single coil by its lonesome in your instrument, you can get more than one sound. Any two or more coils can be wired in series or parallel, and in and out of phase from each other, weather two single coil pickups, or one humbucker (two coils) or more pickups in any combination thereof. Using the right switch, or any number of switches, all kind's of combinations can be achieved.
Here are the basic pickup wiring options, shown on one humbucker, with the polarity and winding direction shown, but it can also be seen as two single coil pickups (one being RWRP). You will normally find that most instruments, use a staggered configuration of normal and RWRP coils, no matter what pickups are used, but it is not an absolute must.
Series:
This is how a humbucker is normally wired in most instruments that only have humbuckers, it has the highest output and reproduces the widest range of frequencies the pickup is capable of, but can sound muddy in some cases. It is not how two single coils are wired in standard applications. For instruments equipped with Both humbuckers, and single coils, the output volumes of the individual pickups are close to each other by design of the pickups, in conjunction with how they are wired, in order to have a good balance.
Parallel:
When a humbucker is wired in parallel, It's output volume is near half of what it is in series, and the range of frequencies it reproduces is slightly lower, but it is also cleaner sounding. With most instruments equipped with any number of single coil pickups they are wired in parallel in switching positions where more than one are on, so that there is no major increase in output volume in those positions.
Out of phase:
When you run two coils out of phase from each other, it is the electrical phase that is being referred to, so it is a swap of plus and minus of one of the two coils.
There are magnetic, and winding phase too, but you are not likely to find that on factory equipped instruments. Neither magnetic nor winding phase can be switched, but instead would require unwinding and then rewinding a coil, or pulling the magnets out and sticking them back in upside down, and neither is much fun. The only way it can be achieved is if you can actually get your hands on an oddball pickup that was made ignoring common standards, and the sound is undesirable by most peoples ears, so it makes little sense to begin with.
Using pickups out of electrical phase reduces output volume a little, but most notable is the change in sound. The out of phase sound is often described as strange, weird, skwauky, squelched even esoteric... at best it is hard to describe, but let me try:
Part of the hum canceling is removed, and frequency canceling is introduced, but which frequencies are affected and by how much, depends on the construction of the pickups or coils in question. The closer they are alike in construction the more the cancellation is spread out through the board of frequencies. The more different their construction i.e. magnet type and strength, wire gauge, and amount of windings, the more the effected frequencies vary. The proximity of the coils to each other, makes a little difference too, as the effect lessens slightly as distance increases.
Using phase switching is hit or miss as far as results, and is not something that anyone has spent much time researching, so you would be hard pressed to find information on the differences of various pickups by manufacturer and type, as used out of phase from each other.
The only real way to find out is to try it, and if you are going to have electrical work done by me anyway, then we can explore the possibility to see if you want the option, as it is a sound that although most people have little use for, others find it worth having, and even a major part of their sound.
Extended pickup wiring:
I don't want to complicate things, but the subject is by nature, and again you don't have to get into technical details, as your sound can be built on your needs with my expertise, but you may want to know this stuff.
Just as individual coils can be in series or parallel, in or out of phase from each other, so can groups of coils and pickups, and the more coils your instrument has the more possibilities there are. You may have seen and heard of trembucke's (a 3 coil pickup), guitars with three humbuckers (six coils) and possibly even crazy guitars with as many pickups as can be crammed into the space between the bridge and neck! I think that Rick Nielsen of Cheap Trick has at least one of each. Add to that a great number of switches, to get all the combinations your many coils can be wired to, with blend potentiometers between them... then it becomes impractical and down right confusing to use.