Generally what and how you shoot and your budget tend to be the three big deciding factors in what gear is appropriate and the best fit for you.
Interchangeable lens system cameras, like dSLRs or mirrorless cameras are generally the most versatile types of cameras, because of the ability to switch out lenses and use hotshoe flashes, etc. But they also tend to be the most expensive, because, well, you have to buy a system, not just a camera body. And the body, in that system, is actually the most disposable piece of gear that tends to get upgraded for a lot of folks, like cellphones or computers, every 3-5 years. I tend to think a beginner starting out with dSLRs should budget anywhere from $1000-$2000 for a basic setup. And that's assuming you get a modest low-end body to start with, leaving at least half if not more of the budget for lenses.
dSLRs, however, are probably your best choice if you plan on shooting fast action (say, sports or wildlife), or need to do something really exotic (like use a fisheye or tilt-shift lens). Mirrorless is better if you need to go small and light and are willing to sacrifice some versatility, since the overall systems are a bit smaller, given that they're much newer systems. dSLR systems can typically leverage film-era gear and lenses.
But there is nothing stopping you from learning photography seriously with a fixed-lens camera. You will be limited to the fixed lens, for sure. But that can be good or bad. It's really good for the wallet to have fewer "add-ons" to buy. And it can be good in pushing you to try post processing techniques like panostitching or HDR. And a lot of fixed-lens cameras have more limited function and smaller sensors, than their interchangeable-lens counterparts, but that doesn't mean you can't shoot pictures seriously with one, or that you can't learn to make up for some of the limitations with post-processing.
However. A $200 budget is a pretty serious limit when it comes to camera gear. You may want to consider whether you can save up and use your phone's camera (if you have one you're ok with) for a while. Finding a $200 new camera that does full Manual mode and RAW is already going to be tough. The more serious compacts with large sensors are definitely out (those cost roughly the same as a dSLR body). And it could be that the only way to get something like what you envision is to go used or refurbished. And that's not a bad thing.
Sensors have been getting really good over the last three to five years, so even getting what would be considered antiquated, like a Canon Powershot S90, or any of the equivalent Panasonic, Olympus, Sony, etc. models would get you pretty decent performance, manual controls, and RAW capability, in a convenient package.
