I feel like I'm resurrecting a really old and irrelevant topic. But here's a random list of ideas (I'm too drunk to compose a comprehensive guide, but really feel like talking cameras to anyone who's willing to listen for the next six hours).
Disclosure: I'm a Nikon user and currently own a D610. Haven't had much experience with Canon cameras, so might inadvertently be using brand specific terminology. I can also make wild assumptions about Canon without knowing it. However, if someone tells you that Brand A is better than Brand B - you can stop listening right there. Those people usually don't understand equipment very well and will often try to justify their reasoning by saying that this INSERT NAME super awesome photographer uses Brand A, therefore it must clearly be better. The reason professionals usually stick to the same brand is because Canon and Nikon lenses are not inter-compatible. Once you invest in an extra lens or two, you sort of get stuck with one brand for life. You can replace the camera body, but spending thousands on a new set of identical in quality lenses makes no sense. A typical scenario in which people consider switching brand is when their entire gear gets stolen.
If you want a versatile education in photography, DSLR's are definitely the direction to go. In my experience, compact cameras often miss out even the most basic settings. I've had experience with cameras that don't have a way to adjust Aperture or Shutter Speed. A lot of the stuff out there is basically what a smartphone with a built in camera can offer. I haven't had any experience with the new mirrorless cameras, but I trust they might be OK, so long as they provide a physical viewfinder. Trying to frame something using a screen in sunlight is usually a pain. I've had a pleasant experience with Sony R1, however. It had a screen that could be rotated all over the place, so it made it possible to get some really low angles without lying down on the ground or from places where I just wouldn't fit.
Don't spend all the money on just the camera. Consider investing in a tripod, some dedicating editing software (Lightroom is fairly affordable), a flash unit, maybe a filter or two, a carrying bag, grey cards and a replacement strap.
A tripod really expands what you can do with a camera. You can do low light photography, HDR, light tracing, cities at night, etc. In my experience, most tripods were fairly similar. Some were sturdier, some were taller, some were more compact, but generally - everything I used had the same problem with taking a little too much time to set them to point the camera where you wanted. Getting the horizon right was usually the biggest pain. I'd set the horizon, secure the camera, let go... And see the horizon skew under the weight of the camera... Until I got one of these: http://www.manfrotto.com/photo-heads-joystick They're pretty expensive, but you should be aware of them for future reference. Makes composing super easy and fuss free.
Software is very important. I understand you've been taking pictures in JPEG and PNG (no lossy compression, but still very similar in nature). What most DSLR's do is allow you to take pictures in RAW formats. JPEG allows you to have 8 bits per colour channel - that's 256 shades. RAW formats typically give you more bits. A 12 bit colour depth will be using 4096 colours per channel. You won't be able to see that on a typical monitor (or even with your typical human eyes, unless you're one of those tetrachromatic mutants) and you'll still be sending people JPEGs for practical reasons, but this gives you a lot more options in post-processing. White balance will become irrelevant. You'll be able to figure that out at home, instead of trying to guess whether you're shooting under sunny 5500K, cloudy 8000K or a 2800K incandescent light bulb. You will also have a lot more room to adjust for any mistakes in exposure. I can just about afford to make super-critical mistakes of 2EV's and hide them as if that didn't happen. That's recording 4 times as much or as little light as I should have, if you pardon the jargon. And here's a cool video where a guy compares JPEG and RAW in terms of white balance: https://www.youtube.com/watch?v=E4X8BhlsxVk
A Grey Card is a "neutral grey" piece of plastic that helps you set the white balance. You take a picture of that under the light conditions in which you are shooting and then use that shot to set the white balance for all the other picture. A piece of decent A4 paper is often a good enough replacement though.
Megapixels are probably irrelevant. A 1080p monitor is displaying 2. A 4K monitor would just about cover the 8.3 megapixel photo from my smartphone (and it would look horrible in so many ways).
Flash is pretty useful, especially if you are doing events or parties. There's always a built in one, but as a rule, it always points in the same direction, casts shadows with large lenses and makes ugly, brightly reflections from people's greasy skin. A separate flash unit gives you more flexibility (you can bounce the light off the ceiling for more natural shadows and to avoid direct reflections) and often comes with attachments like a diffuse filter to create nice and soft illumination.
I won't go into lenses, I think that's either a bit obvious or needs a whole separate post. But you might want to get a filter for one. A lot of people usually get a UV filter. I think it's meant to remove some artifacts like "Purple Fringing", but the main main reason to always use that one is because instead of exposing an expensive lens to dust and accidental scratches, you are only exposing a cheap piece of attachment glass. And do some reading on Polarising ones. They're a bit too much to cover here.
A replacement strap is pretty useful. DSLRs are basically pretty heavy and a typical experience is getting punched in the chest with a heavy object every odd step you make. Not very pleasant. I've replaced the default strap with a Sun-Sniper one. It makes the camera hang comfortable around my soft posterior, gets it out of the way when I'm moving around, leaves it instantly accessible and has a steel wire on the inside, so thieves couldn't use a knife to quickly cut through it and make off with your camera. However, I recommend checking whether it's screwed on tightly every time you take it out. I had my old D90 get unscrewed and drop on the ground once. Cracked the body around the area where the battery goes in (minor crack, I doubt anyone would find it if I didn't point it out) and I couldn't use it until I got a replacement lid for the battery. My own fault, really. I'm using the same strap with the much more expensive D610 now, so it's not a game changer, just something to be cautious of. Here's a good advertisement/review showing off what the strap is all about: https://www.youtube.com/watch?v=SXRkwQG6nto
One of the last things I can think of is the sensor size. There's the "Full Size" sensors, 36mm by 24mm, which match the 35mm film factor. 35mm comes from 24mm height and the additional height of the sides with punched holes in them, which film camera used to roll the film. "Full Size" sensors are only used in high end, really expensive cameras. I don't think there's "Full Size" sensors in any cameras under a 1000 euros (not even counting the lens). Most hobby cameras have cropped sensors. Nikon uses a 1.5 crop factor (24mm by 16mm) and Canon uses a 1.6 one. This doesn't necessarily affect quality directly so much as it does the choice of lenses. The way I understand this area, most high end lenses are made with "Full Size" sensors in mind. I think this is part legacy (a lot of the lenses in the wild are used from the olden days where Digital was not even an option, but are still compatible) and part due to the fact that most hobby photographers who buy a low to mid-range camera never actually bother to change the kit lens for anything else.
You can use "Full Size" lenses on a camera with a cropped sensor without any issues at all, but to me it feels like you're overpaying for lens area you're not using. There's also specific lenses designed for use with cropped sensors which are lighter, smaller and cheaper, but they're not very good if you ever upgrade to a full size sensor. They'll still work, but you will literally be looking at something like a "binocular" view with the four edges being completely dark. Something like extreme vignetting.
Oh! Colour calibration! Almost forgot. Basically, you can have whatever camera you want, but your result will be limited by your post-production. I bet you've seen monitors where you can set the colour scheme to "warm" or "cold" and some additional options in-between. It's a thing of preference, but you should really be wondering about the "correct" way to display colours. There's devices like Spyder and X-rite on the market that help you calibrate your monitor to something like an industry standard. You attach them to the monitor, launch some software that displays certain colours and the devices read what you get on the display. They then create a lookup table for you GPU that helps it make sure that the colours you see are as close to what they're meant to be as possible. You can't guarantee that all your friends on Facebook will see the picture the way you do, but at least the people with calibrated their monitors will. And it's a half-way step to making sure your printouts look right.
Colour pictures are a bit of a personal preference, but as soon as you're dealing with B/W images, it's super easy to spot that some monitors are making them look either bluish or orangeish.
I think I'm running out of idea now. The last bits I wanted to touch were smartphone apps. There's calculator apps that can help you figure out the Depth of Field you might achieve depending on distance and aperture size.
There's also Ken Rockwell's website: http://www.kenrockwell.com/tech.htm I think the guy is a real expert on all things photographic and he was lots of useful articles that could help you with your technique and processes.
There's http://www.lagom.nl/ which will teach you a lot about you LCD monitor. The "Viewing Angle" test will probably be the most disturbing thing you've ever seen on a monitor so far...
And the very last thing... I wouldn't necessarily shy away from used camera on Ebay. If the thing is in good condition, you'll be getting a chance to experience the full advantages of a camera at something like half the price and lose very little resale value over the next few years.
I'm done, but would love to discuss any statement in the post above if you have any issues. Cheers!