Please see What do I need to consider to choose between dSLR, mirrorless, or a compact as my first "serious" camera? first, for the basics on differences between the main types of camera most of us consider to be "serious".

I'm going to focus on the fact that you want to do wildlife photography, and that you chose the one type of "non-serious" camera that might have an advantage for this subject.

Wildlife requirements

For shooting wildlife, you're kind of between a rock and a hard place on a fixed

Mirrorless or an APS-C sensored compact are unlikely to be great tools for, say, birds in flight, (while great for everything else), simply because the supertelephoto lens choices and super-fast tracking autofocus aren't really there yet. And the choices that are there, like the ones on the dSLR side of the fence are much more expensive than your budget (say, $800-$1500 for the camera body, $800-$[price of a used car] for the lens). That's if you're thinking National Geographic-like pics and flightly flitty creatures.

For larger wildlife that's not so shy (or you've got great fieldcraft, use a hide, etc.) or fast, you can get more of a bargain lens (see How advanced is phase detect AF for bird photography compared to contrast detect AF?) and do okay for your budget, especially if you shop used gear, but your entire budget is likely to go for this single subject. So, it depends on how heavily you're concentrated on wildlife photography.

About the choice of a Powershot SX

The Powershot model you've chosen is slightly more casual than most photographers would prefer for deeply learning photography. It's good for snapshots, and particularly good for sunlight subjects out in the daytime. But it doesn't do RAW, so you're more limited on post-processing by only having JPEG capability. And it doesn't have a flash hotshoe, so using an external off-camera flash with it becomes more difficult, which can be problematic for portrait, product, or macro photography.

It's also hampered by a small sensor (1/2.3" format, roughly 1/5th the size of a frame of 135mm film), and a slow lens for low light shooting and shallow depth of field. And its autofocus speed isn't particularly fast.

Lens size, reach, and speed (brightness--how large the aperture opening can be set) are all tradeoffs of each other. Giving a lens a lot of reach, but keeping it small, typically means it's going to have a small aperture. Giving a lens a big aperture and a lot of reach means it's going to have to be big. And making a lens small and fast typically means shortening its reach.

In addition to this, using a very long lens with a lot of "zoom" can be a narrowing window of opportunity. Everything is magnified, including camera shake from handholding. It's harder to aim/compose the shot, because you can only see a tiny bit of it. Without a viewfinder, you're composing at arm's length, destabilizating your hold. Your maximum aperture got small (f/6.9 on the SX you're looking at). It's going to be harder to shoot zoomed all the way in with a bridge camera than you might think. And the "reach" is coming from the small sensor size more than the lens. Image quality may not be what you're expecting, unless you use a tripod or stabilization. Which is more gear to haul.

Small, compact, but with a ton of reach is a hard ask of camera gear. So while the SX can do what you want for low cost, it may not do it as well as you want. It'll be good for macro, though, and landscape in the right light. But low light, portraits, fast action--these are not the type of images this camera excels at.

Consider a 1"-format superzoom

For your budget, I think one class of cameras you might want to consider--although for the same money, if you drop wildlife from the list for now you could probably get a much better overall system in mirrorless or dSLR, you could consider two camera models that are superzoom "bridge" cameras, but are more "serious", as they have a larger 1"-format sensor (1/3 the size of a frame of 35mm film), and slightly faster/shorter lenses. The one within your budget is the Panasonic LZ1000, or the Canon Powershot G3X (outside your budget, but might be affordable a year from now, used). But these would be only marginally better.