....I'd like to get as close to professional shots as possible.
That would be up to you and what you are willing to learn, not the camera.
A dSLR will obviously get better quality results than a P&S, but for "professional shots" as you put it, that is up to your knowledge of photography, not the camera.
If you are willing to learn about photography, then what you need is a camera with manual capability. You can go inexpensive with a "bridge" camera, or otherwise known as a superzoom, or even inexpensive with a beginner dSLR such as the Nikon D40. When I started playing around with photography, I purchased a superzoom. I used it to learn about exposure and how the shutter, aperture, and ISO relate to each other to get the "correct" exposure. I also used it to learn the rules of composition, which is the most important part of "professional" looking shots.
The composition aspect is the part that is learned no matter what camera you choose. A coworker and I both bought cameras at the same time 2 years ago. I bought a $200 superzoom and he spent $1500 on a dSLR package. He leaves his in auto mode everything and I learned the various aspects of photography. Guess which camera produces better shots? Yup, the $200 superzoom because I apply the knowledge of photography to the shots while he lets the camera decide everything and just points and shoots.
That said, you do outgrow a superzoom quite quickly. I outgrew mine in less than a year and it no longer can do what I want. I would like to go dSLR, but funds were not there. Now funds are going to be there for me next year, but instead I am taking the family to Disney for our first vacation ever. I still use that same $200 superzoom and it still does many of the things I want to do. That was two years ago I bought it and the superzooms of today are far greater in capability than mine is.
That would be my recommendation depending on budget. You can get a superzoom and learn about photography that way very cheap. That way you won't have the hindrance of carrying around several pounds of gear and you will learn where you want to go in the future. Or, you can go for a budget dSLR (less than $500 for a Nikon D40) and utilize that to see how far you want to go with it. I wouldn't recommend spending $1000 on a camera that you will just use as a point and shoot such as the coworker I mention above.
For the record, with learning with my little superzoom, I got to understand the limitations of my camera so that I know what I want in a future camera. This will allow me to make a more informed decision at purchasing something much more expensive in the future rather than buying a dSLR based on price then having to sell everything because I found out about a feature I want/need in another camera system.