It depends on your interest and intended uses. (I started with Canon S30 and added a Nkn D70. I still use both.)
If you are fairly new to photography or tend to rely on the camera to control your exposure, I would not select the DSLR. There are tons of cameras in this category that start at less than $200 and go up from there. Many take very good pictures right out of the package.
The advantages of these cameras: a) they have a small form factor; b) the workflow is very easy (subject --> picture --> computer --> printer/email); c) they typically take nice picture; d) you don't need to worry about lens selections and sensor cleaning.
If you like to really control the prictures you take and view this as a craft, a dslr may be the way to go. A dslr is not without downsides -- they cost more, sensors need cleaning, they weigh more and it takes more post processing work to get a better picture. OTOH, it really does put you in charge and you have the potential to take great pictures.
Regardless of which direction, I would suggest trying them out in person (how does it feel in my hand, do the controls make sense to me, how does the LCD screen or viewinder look to me, etc.) as well as reading reviews (imaging reources, dpreview, etc.). Considerations include: a) how fast is the lens; what is the range of the lens; how shar is the lens; how much user control does it offer; how much resolution (megapixels); what software comes with it; what is the shutter lag like; does it take filters; and does it offer the types of controls you are likely to need/want.