I"m really interested in starting up a hobby and photography has really been appealing to me since I've went on a few hikes with friends. There are just so many moments I'd love to capture and places I may not go again. Photos keep that moment in a standstill and you can think back on it.

Since I'm only beginning and all I would love to get some input on a good camera that would be around $200 and under range?
Mostly I want to shoot pictures of things I see along my walks and hikes. I also have a beautiful active husky who never stands still for even a moment, I'd love something that would be able to capture her in her still active moments as well as work for the other things I want it for.
Any advice would be appreciated!
In general, your question asks the basics of "I want a new camera". Your specifics, however, say you want a rather specialized camera. Capturing an active animal in motion is difficult for even some more experienced photographers using more specialized (and expensive) gear.
Your budget says you can't afford specialized gear.
At your stated price range you might be better off simply using a decent smartphone camera and acquiring a photo editor to do much of the work in post production via your computer system.
Any digital camera you use will require (or certainly benefit from) some work at your computer to achieve the best results and you might want to put your money into the editor first. Then save for a better camera as your experience grows.
Otherwise, I would tell you to seek out a local photographic equipment retailer who takes trade ins. Spend a weekday or two (not a weekend when the shop is busy) discussing their used, trade in equipment.
Like a car, cameras take a fairly large hit in depreciation after the first few years. Allow someone else to absorb that hit and consider a DSLR that is several years old. Unless you intend to enlarge your shots to wall size hangings, even a decent DSLR with a 8 to 10 megapixels sensor will be sufficient. That sort of camera should be available for under $200.
That may not, however, get you a lens with the camera, just a working body.
People also trade in lenses and there will be numerous kit lenses to choose from I suspect.
"Kit lenses" are provided by the camera manufacturers as an all inclusive way to simply get someone up and running if they are not overly interested in image quality. They would be fine to begin with though you can do better.
"Better" in your budget will mean a non-zoom lens. The Canon 50mm prime lens would be a good choice though the combined cost would be slightly over budget.
The 50 mm is "fast", meaning it can open its aperture to a wide setting which will allow in more light and enable you to capture those images of your dog in motion.
50mm isn't the best choice though for those landscape shots you might find on your hikes. This is something you will need to discuss with the retailer and why this might take more than one visit to the shop. If you do not understand the lingo being used by the shop, ask them to explain in plain English what they are saying. Taking notes is never a bad idea when doing this sort of shopping.
If you spend time with your local shop, do buy from your local shop. After the sale service and advice will be both beneficial and needed in most cases.
Handle the cameras available and look through their menus. The menu is the pathway to making your camera do as you tell it.
If you can't easily navigate the menus, you can't get the shot you want in many cases.
IMO Canon has the best menus for a newbie, with Nikon a close second. Choosing either of those lines as your base will also allow you the broadest selection of (pre-owned) gear and accessories to fill out your needs.
Alternately, if you only want a camera and nothing all that special other than it takes decent photos, look at an "enthusiast" compact. Small and light but with the amount of controls needed to take a decent photo, they are good for the hiker who travels light. IMO the best route there is to look at the Canon "S" and "SX" series of cameras; mshop.usa.canon.com/shop/en/catalog/refurbished-powershot-digital-cameras#facet:&productBeginIndex:0&orderBy:11&pageView:grid&minPrice:&maxPrice:&pageSize:& (Refurbished cameras from Canon or Nikon come with a warranty. The selection varies weekly with the availability of new stock so check back if you don't see what you want.)