I'm in the process of getting my first electric guitar and am trying to figure out amplifiers. I currently have a stereo amplifier and pre amplifier and a pair floor standing speakers. My living space isn't large and I'm curious if I can use my existing stereo equipment with a guitar. I'm no audiophile so as long as it sounds decent I'd be happy (I plan on playing with headphones mostly anyways). Can I use my amplifiers alone? Should I look into purchasing a head amplifier? Or should I get a combo amplifier?
If you're just starting out, I suggest you buy an "amp modeller" such as the Line 6 Pocket POD, which is very small and is sure to fit in. You can use this with headphones or plug it into your stereo and it will sound fine. It's not a guitar amplifier exactly - it's a device which simulates a guitar amplifier and produces an output suitable for home stereos or headphones. Devices like these have many options for different guitar sounds.
Guitar amplifiers and speakers are somewhat different from hi-fi amplifiers and speakers and are an integral part of the overall sound of an electric guitar. Just plugging the output of a guitar into a normal hi-fi will sound wrong, as will plugging the output of a guitar amplifier head into either the hi-fi amplifier or directly into the hi-fi speakers. It's worth mentioning that the latter two of these options may also damage your hi-fi equipment!
Some people feel that amp modellers don't feel like a "real" guitar amplifier. In this case, the only answer is get a dedicated guitar amplifier. This could be a combo or a separate head and speaker cabinet.
For a beginner I would recommend a small and simple practice combo. Specifically a Roland Micro Cube. This will give you lots of options for tones (clean, amp stack, overdrive, distortion), built in effects (chorus, phaser, delay, reverb), and you won't have to spend too much time fiddling with knob settings, which means more time spent practicing. Very important for beginners, as I fell into the gear trap when I first started playing. I should have practiced more and tweaked effects and amps less. Know I know. A Micro Cube will have everything you need for some time.
Best part: it is built like a brick house and will last for years, but is not expensive.
My first 2 amps were a 150 watt combo, which I still occasionally use 25 years later - which is almost indestructible, but doesn't have the clearest sound in the world, and a full sideboard sized radiogram, with magic eye tube for tuning - I just wired a socket into one of the input stages.
I have to say, playing my guitar through that tube based hi-fi was one of the sweetest sounds ever. Until it died - it was very old.
After that I cannibalised an early Sony Walkman, wiring a jack socket in place of the playback head. That gave a nice distortion through headphones and didn't annoy the family/neighbours.
The matchbox sized Vox amps are also inoffensive and have a decent enough sound.
tl;dr - you can use anything - it's all good at beginner stage:-)
Welcome to SE and to the world of electric guitar!
You can also get amplifier modeling software - like Amplitube (which is free, for some values of free). With that, an instrument interface for your PC, and some cables from the line-out on your PC, you can easily use your existing stereo equipment with your guitar - or headphones right out of your PC.
I have used the Line 6 Pocket Pod, which I like very much (But be forewarned: It has a huge battery appetite! Get an AC adapter!) in exactly this setup when my brother was in town to get a second amplifier.
I have also used a Line 6 TonePort (now Pod Studio, I think) with the accompanying software (It used to be Gearbox, I got a free Pod Farm upgrade at some point, don't know what the status of software is now) for both playing (esp. playing along with online lessons) and recording. I only record myself for educational purposes. I have no illusions.
If I were buying a piece of gear now and wanted to not have a traditional amp, I would probably pick up one of the DigiTech pedals - like the RP255. It has a bunch of amp and effect modelers, a looper, a headphone jack, a USB interface, a drum machine, and a regular instrument out that you can use when you get another amp.
Any of these solutions should be more than enough for you to get your feet wet and make a more informed decision if and when you feel that you have outgrown your current rig.
I played for three months with NO amplification when I started as a service to my family and neighbors!
In addition to mark's answer:
As, mark stated corretly, a guitar amplifier is not interchangeable with a HiFi-ampflifier (like your stereo).
Now it's important to know what's your budget and what do you want from your sound. You said you're a beginner and so I guess you planned to use a smaller budged and you aren't yet obsessed with true valve sound.
You can basically divide the amplifier field in 2 sections: tube-amplifier and transistor amplifier. They're based on two different kind of circuitries. They have the following basic pro's and con's:
There are also hybrid-amplifiers (called: solid-state) on the market, which are cheaper than tube amps and (generally) better sounding than transistor amps, but on the other hand more expensive than transistor amps and a bit colder sounding than tube-amps.
"Normal" amps are usually quite pricy if you want to have a half-decent one. But there is another alternative: (And it's more versatile, which is good for a beginner) A modelling unit! (mark already suggested it)
A modelling unit is a more a computer than a "normal" amplifier. The sounds are emulated versions (usually) of well-known tube- and (in some cases) transistor-amplifiers. They usually have everything you might need built in (tuner, effects and so on), but cheaper models tend to sound cheap. (state the obvious) They come in different packages and price-ranges. "Single-units" (not sure if that's the right term) are usually good to use with a normal stereo, your headphones, for recording purposes, or even as preamp for a guitar-amplifier. They have NO cabinet, and no power amp!
And there are modelling-amplifiers who use a modelling built in a head or combo. There are good and affordable practictice amplifiers. I'd recomment you check some of these out: Roland (micro) Cube, Peavy Vypyr, Line6 Spider.