If you want to make the jump to something more capable I recommend skipping all the stuff in the middle like mirrorless, 4/3, or high end point and shoot. Nothing wrong with these if it is what you want. However, I recommend you get a digital SLR. Decide on a budget. If it is small, buy used. Heck if it is big it still doesn't hurt to buy used. Especially lenses and tripods. I have never purchased a new camera, lens, or tripod.
Prioritize your purchase in this order:
- A book about the photo style that interests you.
- Lens or lenses. This is the most important thing. It doesn't matter how awesome your camera is if you are sticking low quality glass on it.
- A good tripod you can tolerate carrying for extended periods of time. The number one thing you can do to take better pictures is to use a tripod. For most, tripods are an afterthought.
- A digital SLR body.
I recommend this order because lenses are very long term investments as are tripods. They can last a lifetime. Bodies churn constantly and you can always get a better one later.
If I were going to buy a DSLR today, most likely I would choose Nikon (but I'm already invested in Nikon glass). I would probably go for a D750 (D700 if money is tight, or a newer variant if I'm feeling flush) and a 50mm f/1.4 AF-D. If I wanted to shoot portraits an 85mm or so would be my next lens. Otherwise I really like the 35mm f/2 AF-D for landscapes and general use. All of this said, I don't think you can go wrong choosing from any of the major manufacturers. Favor full frame over crop sensors.