Others have given good advice but, I thought I would go into some detail, as this seems to be an area you aren’t familiar with.
Just to be clear, regardless of whether he wants distortion or not, he will need an amp.
Playing an electric guitar without one is pretty pointless other than for occasional scale practice/warmups (but even those should be done with an amp where possible).
Now the good news is that guitar amps come in many forms, as others have indicated.
Detailing some of the main options:
Standard analogue guitar amp (solid-state or valve)
The two main types are combo (meaning they include both the amplifier and the speaker) amps you can also get separate amp “heads” and separate speakers. Most people go for combos.
These tend to be fairly large boxes because you really need at least an 8 inch speaker for these to sound good, and many amps come with a 10 or 12 inch speaker.
There are some smaller units, such as the Vox Pathfinders and others, and there are some smaller amp heads that you can pair up with a mini cabinet, such as the Orange Micro series. This is mine. It sounds decent, and it gets pretty loud, but the sound from the 8 in speaker is fairly compromised:
One advantage is the amp head is quite small and you can plug it into any sized cabinet of the right impedance, so I could take it a rehearsal room and plug it onto one of their speaker cabinets.
One thing to realise is the power output claims of guitar amps should largely be ignored: they are relatively meaningless. In reality, how loud a guitar amp gets isn’t just about the power output, but about the amplifier circuit and speaker efficiency. There are some 10W guitar amps that will be louder than other amps which claim to be 50W.
Whether the amp directly supports distortion or not depends on the amp. Some amps don’t really have anything other than a mild overdrive, whilst a Laney amp I used to own simply would not do clean tones at all.
Within this category, the only real difference between a “Practice amp” and other amps is how big they are and how loud they get. And what people consider to be “practice amps” is largely a matter of opinion (my Laney was considered a practice amp by some, but it was a 15W valve amp and I couldn’t turn the volume up above about 2 at home without damaging my ears).
Most amps of this sort will do overdriven tones, but to get “high-gain” or distortion it’s normal to do this with a separate pedal.
A lot of amps in this category don’t have headphone capability, and many of the ones that do don’t have a good-sounding headphone capability.
Full-sized Digital modelling amps
These are amps which are a similar form factor to the standard analogue amps (and similar sizes) but which use digital modelling technology and solid-state electronics.
The advantage of these is that they tend to be physically lighter, but also far more versatile as they not only model multiple styles of analogue amp, but usually also include a bunch of pedal emulations, so you won’t need to buy separate pedals to get all sorts of overdriven and distortion tones.
They also often have other capabilities like USB recording (so you can record without buying an audio interface) and they normally have decent headphone outputs. Some have Bluetooth so you can stream music to them, although in my experience in this category, it’s something you would only do for backing tracks, rather than for casual music listening.
And they usually will work at low volumes so you can use them both as a “real amp” for rehearsals with a band, as well as at low volumes for home practice use.
Popular amps in this category include the Boss Katana 50/100, The Fender Mustang series, The Fender LT series, Blackstar Core series, and many others.
Digital Modelling Practice amps
These are small, quiet amps dedicated for practice. These are really good if you need portability or don’t have a lot of space. I’ve been using my Yamaha THR10ii for the last couple of years in various apartments where I really couldn’t use a bigger amp. And it’s also portable enough that I can carry it as hand luggage on airplanes.
In general, these things do not get loud and are unsuitable for band practice or gigging. In some cases it is possible to plug in an external amp or powered speaker cabinet, but, in general, your options for this are fairly limited.
They come in a range of sizes from pocket-sized up to something larger than a shoe box.
They share a lot of characteristics with their larger cousins, but the sound quality from them is not naturally as good as they tend to have smaller speakers (5 inch or less) and use digital processing tricks to make them sound more like a proper guitar amp.
They tend to be simpler to use and have fewer capabilities than their bigger cousins, but that’s not always the case. Some of these amps really require an app to use them properly, so if messing with phone apps is a problem, that’s something to look out for.
In this category, most of the devices also support Bluetooth streaming, and they are very suitable for using to listen to music; they will give similar quality to a Bluetooth speaker of a similar size.
Some of these have options for battery use and wireless.
Devices in this Category include things like the Boss Katana Mini and Air, the Positive Grid devices, the Nux Mighty Space and Air, The Yamaha THR series
Headphone amps
These are portable units which have no speakers of their own and which, commonly, plug directly into the guitar. They are pretty much always digital modelling systems and have similar capabilities to practice amps (including, in some cases, Bluetooth streaming).
These can be connected to an external amp (like a home stereo) if you want, but the primary use for these is for headphones, so I wouldn’t consider these if he is likely to spend an significant time playing without headphones.
A lot of these are cheap enough that you can get them alongside another amp.
Most of them will need an app to control them.
Devices include the Vox Amplugs, Boss Pocket GT, Nux Mighty Plug, Fender Mustang Micro, etc. Also the Boss Waza Air which is actually a set of high-quality headphones with the guitar amp built in.
Multifx systems
These are, basically, similar to the headphone amps in that they are a digital modelling system without any speakers. But these are, almost always, floor mounting units with switches and, sometimes, expression pedals to allow them to be foot controlled.
These can either plug into a normal guitar amp to provide extra effects and tones, or into headphones. They can also be connected to dedicated speakers systems known as FRFR speakers.
These units are very common, with a wide variety at all price ranges from around $100 to $1,500 or more depending on the quality and capabilities you want.
Frankly, even at the low price points, many of these units are really good.
Examples include the Zoom series (G1X Four, G3, G5, etc.), Boss range (GT-1, GX100, GT1000, ME90 etc.), and units from Valeton, AxeFX, Neural (Quad Cortex), Line6 (Pod Go, Helix range), Fractal Audio (FM series), and Fender (ToneMaster Pro).
My personal view is, if you have the space for it, a Boss Katana or Fender Mustang would be a good choice for a versatile amplifier with more effects than you can shake a stick at, and the ability to be cranked loudly, but also to be used at bedroom volumes or with headphones.
If you just want headphone use, a headphone amp or a multifx pedal board. the former is more portable, but the multifx unit is more flexible and can be used without an app.
For a headphone amp, I would recommend the Nux MP3.
For a cheap multifx device, I think it’s hard to go wrong with a Boss GT-1. I’ve been using one for years and they can sound pretty good, are quite portable, and I’ve seen a fair number of gigging musicians using them (and Boss pedalboards in general), including this one:
Cheers,
Keith