What you are looking for is NOT a fiber channel switch. You are looking for an ethernet switch with SFP slots, unless you want an antique (GPIB slot). While you can purchase SFP switches with no copper slots, it's often not the best or most affordable solution. Then you need SFPs (Small Form Pluggables) which are the devices that actually connect to LC fiber optic connectors and plug into the slots.
On the low end you can get Gigabit 8 copper 2/SFP ethernet switches for $100 each, or less. Be careful not to buy 100Mbit when shopping used stuff. Much larger than life, an SFP:
An SFP switch (this exact one possibly no longer available new, but there are many, and used works fine in most cases anyway) with 16 copper and 4 SFP (fiber) slots
With no connectors in place, if going there, use LCs - everything "modern" does. But you'll find the process is rather expensive to set up for doing, or to have done.
You also need to figure out what your fiber is (singlemode/multimode - & what core size (50 or 62.5) if multimode, and whether it's OM3 or 4 if it's 50), so you can buy the right SFPs, and you'll want to carefully look on ebay to see if you can find some at a reasonable price. It's not a small undertaking (I got a baptism by needing to do a large project with virtually no budget 3-1/2 years ago.)
If your house is not huge, there may be a simple wiring issue with not getting full throughput on Cat5e - it should be good for gigabit up to 100 meters - 328 feet. That would be lot cheaper to solve than terminating a bunch of fiber, unless you have the tools already, which seems unlikely. Often electricians who are not network techs mess up Cat5e installs, IME. Phone techs are (or were circa 2004) prone to use Cat3 or Cat5 jacks since many of them did not stock Cat5e jacks and few customers were actually using gigabit then to notice - that might be the first thing to check. Better switches can also be set up to trunk several copper connections (if several connections are available between places you want to go) to provide 2, 3, or up to 8 GB over copper.
To clarify a bit with more space than is in comments - fusion spliced no-polish (prepolished) conectors are OK, but expensive (both to buy and to have the equipment to use, though you can rent a splicer.) A fusion splice is, in most cases with a modern splicer, a good splice. The field-termination mechanical splice connectors are great in the eyes of the salesmen, and nobody else...a mechanical splice has several issues right from the get-go, and despite the protestations of the salesmen, real users find that the index-matching gel used to make them somewhat better than they would be without it dries out, turns brown, or both over time, making the connector lose light transmission ability. Epoxy polish (where the actual fiber is inserted in the connector and held with epoxy, then polished in the connector) is as good as you can get if you actually need a connector, assuming you do a decent polish job (not all that hard if you follow the correct procedures with the correct abrasives.) If you don't need a connector you can disconnect, a fusion splice is better.
One of the most important things to think about when you are planning a fiber optic project is, "how am I going to attach my fibers to my lights?" It's crucial create a clean strong connection between your light source and the ends of your fibers so that light shines directly into the fibers and makes them glow as brightly as possible. A big challenge in this is the fact that the fiber optics themselves are quite slippery and don't adhere to most glues very effectively. I have found that superglue and some epoxies seem to stick the best, but you have to be careful not to get superglue on the end of the fibers where is can cause clouding that effects light transmission down the strand.
As I mentioned in the previous step, standard 5mm diffused LEDs are fairly easy to attach to fiber optics because you can slip a heat shrink tube over both the LED and the fiber optic bundle, shrink it down, add a little glue and you have a fairly strong connection between the two (see first photo). You can buy RGB addressable LEDs in this form from places like Adafruit, so you don't need to sacrifice programability. This Instructable also shows how to achieve a similar connection using Sugru instead of heat shrink.
If you are using LED strip to light your fibers, connecting them gets a bit trickier because the LEDs have such a low profile, there isn't much to connect to. Everyone I know who works with fiber optics seems to have come up with their own solution to this problem.
Ashley Newton, who first introduced me to side emitting fiber optics, and worked with me to create my Sea Warrior outfit, has a very effective method that involves 3D printing a piece that holds the LED strip and has nodes with holes that the fiber optics plug into above each pixel (see photos 2 and 3 above). Variations on this shape can be 3D modeled to fit the form of what you are creating. I talk more about this method in my Fiber Optic Sea Warrior Instructable.
For a recent project I also created a double sided version of these LED nodes that holds a folded LED strip allowing fiber optics to emerge and be illuminated from both sides (photo 4). In another piece of the same project I used 3D modeling to create a module that held a 12 a neopixel LED ring with holes above each pixel for a bundle of fiber optics (photo 5).
Jenn Mann who also makes amazing fiber optic wearables, has found a way to use layers of laser cut acrylic to create a similarly shaped connecting strip between LEDs and fibers.
For my Fiber Optic Fairy Wings, I used a much simpler, and slightly jankier, method. I bundled my end glow fibers into groups of about 30, then heat shrunk the ends together and cut them with an exacto knife to create a smooth edge. I installed my LED strip inside a small box with holes drilled in the sides, then fed my fiber optic bundles through the holes and hot glued them into place up against the LEDs, being careful not to get any hot glue between the ends of the fibers and the LEDs as that would block light from illuminating the fibers (last photo).
This worked fairly well, though some fibers in the middle of the bundles were still loose after I had glued them in. Since I was going to be sewing all my fibers down very securely anyway, this didn't really matter, but I would like to find even better ways make sure all the fibers are secure.