Reddit mentions of The National Gallery Van Gogh Watercolor Paint Set, Plastic Pocketbox, 12-Half Pan General Selection, Sunflowers

For someone just starting out, quality paper is the most important thing followed by paint and brushes. I recommend shopping online as you'll pay 2-3x more locally (unless you have a Blick store nearby, they usually match their online prices) and you can set your girlfriend up nicely without breaking the bank. I'm not sure what you're looking to spend so I'll try to give you a decent range of options.

Paint

Cotman and Van Gogh are the student versions of professional brands (Winsor Newton & Rembrandt) and the most often suggested for beginners. They come in pans (dried paint blocks you swipe with a wet brush to reactivate) and tubes. Though these are student grade they're both used professionally and very high quality. They're lightfast (won't fade with exposure to sun), use the same pigments that the professional brands do (though with a smaller amount) and are both very reasonably priced. And if she enjoys painting and looks to upgrade in the future, she could pick up the Professional version with minimal relearning how the paint performs (All brands behave a little differently on paper).

Of the two I would suggest Van Gogh as they're extremely vibrant, the pans are very easy to rewet (Cotman pans are difficult to get pigment from in my experience, and for someone learning to paint having to scrub a pan with a brush will be frustrating. The tubes better.) and come in nice compact travel sets that have a built in palette for mixing. The Set of 12 Pans is plenty to start with, you can mix a wide variety of colors from that. The 18 pan + 2 tube set is a great option as well as it gives you a nice variety of warm and cool primaries as well as convenient greens and earth colors, it comes with a small brush and sponge, I'd go with that one. The larger sets of 30-48 aren't necessary as they're mostly colors that are mixed from the single pigment paints included in the smaller sets, but if you think she'd enjoy having a ton of colors available without having to mix those are something you can look at too.

If you wanna ball out a little bit and get her some professional paints, Da Vinci has a ton of pan and tube set options. The 12 Full Pan Set again has everything she'd need getting started. They're as good as any brand out there. The pans are also twice the size of the student brand options and will last a very long time.

There's a ton of great paints out there, I suggest these because they're great value as well as quality and don't include a lot of the weird and rarely used colors you find in a lot of sets. I'd go with pans because they're ready to go as soon as you open them, you don't have to wait for the tube paint to dry for a day or two before you can store it or take it with you, they're very attractive gifts that are nice to look at (if you look on youtube you'll see 100s of videos of people just opening them and showing them off) and you can refill them with your own tube paints later on once you know what you like and start building your own palette. This time of the year there's tons of deals out there so if you find a nice set of Winsor Newton or something on amazon that's a great snag as well. Just avoid "store" brands like Artist's Loft or Masters Touch, or the tons of really cheap chinese sets you'll find online.

Paper

100% Cotton is the way to go. It can handle any technique and can take a ton of water without buckling or falling apart. Even the nicest paint will appear dull on poor watercolor paper and they can't handle much water before they start to give out. It can be a little pricey but it's well worth it. Again there's tons of brands but Arches is the most used and it's excellent so I don't wanna bog you don't with a bunch of brands. You could also grab a 22x30 inch sheet of Arches and tear it into a variety of smaller sheets (this is the most common and frugal way). Cold press is medium textured, Hot Press is smooth and Rough is obvious. Cold press is the most versatile so I'd start there. I don't use sketchbooks but if you're looking for something like that I've heard these are good.

Brushes

Brushes are personal preference, some people only use one for everything and some people like a variety of size and hair types. If you wanna keep it simple a 10 or 12 Round is a good workhorse that can handle small detail and a larger wash. There's sets if you wanna get her a few to see what she likes. Synthetic or a blend is where I'd start as real sable or squirrel is pretty expensive. There's water brushes that aren't "traditional" but are popular for sketching or coloring ink art and are easy to use.

Hope this helps!