Looking to buy my wife a camera as the start of a photo hobby. Need recommendations/advice?

You are talking about a digital, single-lens reflex camera, or DSLR. Any of these will give you the features you want. There are two drawbacks: price and bulkiness. Many beginner couples who overcome the price issue find two years down the road that the camera is a pain to tote around because of its size and shape, so instead of documenting the kids, it is sitting on the top shelf of a closet somewhere.

Another thing to think about is focal lengths: SLR owners accumulate an assortment of lenses if they are interested in more than one type of subject. For snapshots of the kids, a single 50mm lens is perfect. If you enjoy artsy close-up shots of the petals of flowers, you need a "macroscopic" lens. But for pictures of your travels you will want both a telephoto lens of 200mm or more, and a wide-angle (panoramic) lens - ideally 18mm. (Anything less that 18mm begins to look too distorted for most viewers to enjoy.) At least THREE lenses, plus the camera - talk about bulk! Over the last 30 years, lens manufacturers have tapped into strap-weary photographers by offering zoom lenses that give you all of that in one lens.

But now we are back to capabilities that are electronically available (approximately) in some pocket cameras that you are more likely to actually keep and use. So: You and your wife might be ahead of the game to go to a store that has a wide range of camera types on display, and actually handle them. THEN decide whether you want a DSLR or a high-end pocket camera. After that, it's simply a matter of entering "best pocket camera" on your browser.

Be sure to understand the camera's low-light abilities, and how to get your images off the camera and into your computer. The good ones no longer require you to physically connect them or move cards between them - but the process can require extra software or hardware. And check out whether they can mimic a phone's ability to take a picture or video and immediately MMS it to a friend. Not all of them offer it.

Good luck!

Indeed DSLRs are the tops, but look also at upper level bridge cameras with physically large sensors (not just lots of megapixels). For instance the Panasonic TZ 1000.

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If all you can or want to spend is $200, then skip a new camera and buy a used Canon G series. Any $200 camera on the market new is not any better than a common iPhone. It won't let you take the kinds of shots that you'll want to take. Do yourself a huge favor and up your budget to around $600 and get a mirrorless camera like the Sony A6xxx series, or a DSLR. There are no bad DSLRs, so anything that's in within your budget will be a good choice. You''ll also want to get a 50mm f/1.8 lens ($140) to take those natural light shots. It'll be very difficult to do that with the 18-55mm kit lens. Pentax's DSLRs and some Sony mirrorless have sensor stabilization which means that the image is stabilized regardless of the lens. If you think this is what you'd need, and it probably is, I'd look at the Sony A5xxx or A6xxx series of mirrorless camera with in-body image stabilization or any Pentax DSLR.

Unless you buy used camera it is unrealistic to expect to get an interchangeable lens camera for $200.

Eg. add an 18-55mm lens to this one:

https://www.keh.com/shop/nikon-d3100-digital-camer...

Sony DSC-HX300

I think it's discontinued but used runs about $300. You can't add lenses to it.

I decided to mention it as a possibility because my wife loves hers and uses it for cat pictures, grandchild pictures and out into nature. She thought she'd not like the inability to attach lenses but she got over it. Especially given the awkward nature of having to carry the lenses and swapping them on and off the camera.

Best wishes with your decision.