I was in a similar position about a year ago, and spent a lot of time asking questions, testing out cameras, and even talking with a few professionals that I know.
I eventually settled on the Canon Powershot S3. It's not a dSLR in the traditional sense because of the built-in mega-zoom lens and some of the built-in "point-and-shoot-like" features, but it does offer a lens attachment that will let you pop on any lens or filter you want to use, and can be set up to offer full SLR control.
I was leery about dropping that much money on a camera that I hadn't actually used, but I'm glad I did. It's a fantastic camera, and has more features than I could ever be reasonably expected to master.
The one thing I think you'll like in the S3 while making the transition from a point-and-shoot to a SLR style is the diversity of the control set. You can set it to act like an SLR, a point-and-shoot, or somewhere in between (so that you only have to worry about one aspect of aperture, or "film" speed, or shutter speed, etc.), or set it to a certain shot mode (night, action, bright light, vivid color, etc.) and just take the shot.
To touch on a few of the pros and cons:
The LCD is a little small by today's standards. However, the 180-degree flip and 360-degree rotation of the screen is VERY handy. I've also found that using the optical viewfinder is more my style anyway. (And unless you're sitting on a tripod, you'll want the extra stability that comes with holding the camera against your body somehow. In my experience, holding the camera away from the body to look through the LCD tends to create blurry shots.)
The single-handed grip is SO comfortable. Even more so than most of the cameras priced twice as much as the S3. The shutter button and zoom control are perfectly positioned and angled for one-handed operation.
Shutter lag is almost imperceptible, and the rapid-fire shooting is more than adequate even in low-light situations.
The only real drawbacks are extremely low-light shooting and image quality with ISO ("film" speed) settings in the 400+ range. (In simple terms, the lower the light, the higher you typically set the ISO number.) If you want a good, crisp shot, you need good lighting. I don't know if this is the case with all dSLRs or not, but compensating for low light results in an image that either lacks contrast or has some added graininess.
Added bonuses are the ability to capture full motion video with stereo sound (about 15 minutes will fit on a 1GB memory card), and you can take high quality pictures WHILE capturing video, shutter timers, repeat timers, built-in flash with expansion flash slot, and so forth.
Cnet also has a great review of this camera: http://reviews.cnet.com/Canon_PowerShot_S3_IS/4505-6501_7-31740582.html
In any event, I've tried some other cameras since I bought this one, and have yet to regret my purchase. For the money, it's the best out there.