What is Reddit's opinion of Lighting for Digital Photography: From Snapshots to Great Shots?
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If she's into portrait photography, I say get a Godox TT685 II-N. Aka the Zoom II AA R2 TTL speedlight at Adorama. And Syl Arena's book, Lighting For Digital Photography.

It's in Godox's X system, so if she wants to go forward with studio-style off-camera lighting, Strobist-style, it has all the built-in radio triggering to do so. And it's a full bells'n'whistles TTL/HSS capable speedlight for on-camera bounce flash use all on its own.

I wouldn't recommend going for anything cheaper than this on Amazon, because it'll either be a single-pin manual only speedlight (no automated modes, no real camera/flash communication other than "fire", and a PITA to use for event photography), will only have a head that rotates 270º, not 330º (hard to bounce at all the angles you want), and may not do HSS (moot with a D3200, but if she upgrades to a camera body that can do HSS, it would be nice if the flash can do it, too).

>Get the book by Bryan Peterson called "Understanding Exposure".

His Learning to See Creatively is also a good beginner's composition guide.

However, I would warn the OP NOT to get Peterson's flash photography book. That one stinks. He's primarily a landscape photographer and his knowledge of flash is minimal. For flash, I'd recommend Syl Arena's Lighting for Digital Photography and of course, the old warhorse college textbook standby, Light—Science & Magic.

Two books I like are the standard college textbook, Light: Science & Magic, and Syl Arena's Lighting for Digital Photography.

But I wouldn't recommend starting there. I would recommend starting with a hotshoe flash and on-camera bounce flash. Neil van Niekerk's Tangents website is a great place to start to learn that. But it also comes in book form. :)

Start with on-camera flash, rather than off-camera studio flash, because all you'll have to buy and learn at first is the flash. And you are going to have to rearrange your exposure think to master flash. Being good at M mode on the camera is just the start.

Whenever you take a flash photo, you are basically combining to exposures: ambient (all the light that isn't from the flash) and the flash. Kind of like two layers in Photoshop.

The ambient exposure is controlled by iso, aperture, and shutter speed (as you know).

The flash exposure, however, is controlled by iso, aperture, power, and distance (of the flash to the subject). Note how shutter speed isn't included. Because, at sync speed and below, the flash burst is much faster than your shutter speed, leaving the shutter open for longer only gathers more light from the ambient, not the flash.

And these differences in control mean you can balance the flash against the ambient however you want (within gear limits).

There's also the fact that your camera's meter can't actually measure your flash while you're composing the image, because the flash burst isn't in the scene yet. It can only measure the ambient light level. So, getting your meter's needle to "0" doesn't necessarily mean a good exposure any more. The only way for the camera to meter the flash is to use TTL (through-the-lens metering), where (with digital) the camera tells the flash to send out a small known-power level "preburst" to meter, meters it, and based on the results, adjusts the power level of the flash accordingly.

A lot of studio lighting gear (particularly the low cost stuff) is "manual only" and doesn't do TTL. Godox is sort of an exception, here, but even with Godox the TTL stuff is more expensive than the manual stuff. But an on-camera speedlight can get you TTL capability relatively cheaply vs. the studio gear.

And you can also follow David Hobby and "go Strobist" by taking a speedlight off-camera as your beginning point to learning studio lighting. Here, the Strobist's Lighting 101 is a great resource, as are David Hobby's Lynda.com Flash Photography courses (your public library, school, or job may get you free access).

For a first or only flash, I'd recommend one that does TTL/HSS, so you can use it both on- and off- camera with equal facility. Most TTL flashes can do M, but Manual-only flashes can't do TTL. My blind recommendation for most folks would be a Godox TT685 (US$110), or if you're shooting mirrorless, maybe a TT350 mini speedlight. Master on-camera flash. Then a single off-camera flash. Then multiple off-camera flashes in studio setups. Walk before you run; run before you fly.