$700 is a tight budget for wildlife, but is doable. You’ll have to buy used; I buy all my camera gear used from reputable dealers or manufacturer refurbished though, and I’ve never had a problem.

I think you have two good options at that price point - a used bridge camera like the Nikon P950, or a used DSLR with an older long focal length lens. The former is going to be smaller and offers more magnification at the expense of image quality, while the latter is going to be larger and heavier.

For the latter option, no matter the brand, you should try to spend as much of that budget on the longest and widest max aperture lens you can find, and then get the cheapest compatible camera body that has the minimum features you need. When it comes to wildlife, money goes much further on lenses than it does on camera bodies. I’m only familiar with Canon though, where your best bet might be an EF 400mm f5.6 (~$600) and a 40D camera body (~$70). That combo is a little low on megapixels and you won’t be able to zoom in and out with that lens, but it will still be more than capable of capturing stunning images at a good distance; wildlife photography YouTuber Duade Paton uses that camera to great effect in a number of budget-oriented videos.

With enough money you can get lenses that are long and fast. Otherwise, you seek out good light; one of the biggest tips for beginner wildlife photographers is to go out at the right time of day. Direct sunlight an hour or so after dawn is more than sufficient to freeze motion with minimal noise, even at a reduced aperture on an APS-C camera body (400mm, f8, 1/2000s, ISO400).

Flashes used to be common - early digital/film era wildlife photography books I’ve read suggest that a flash is a necessary tool - but seem to be dwindling. Use of denoising software is also common.