Digital SLRs and Compact Cameras both have their place. Over the last year or so, I have upgraded both my DSLR and my Compact and make heavy use of both. The former is particularly useful for the many model shoots we do as well as some commercial portraiture. I try to have my compact camera with me at all other times so I can grab photos whenever I get the opportunity.
Bottom line is that modern Digital SLR systems with half-decent lenses are faster at startup time and focusing than ANY compact digital camera.
The focusing mechanism is faster on DSLRs because they work against the optical image whereas compact cameras do their focusing based on processing of the sensor image. A DSLR has a mirror @ 45 degrees in the way of the image sensor that redirects the light up to the eyepiece. The mirror also lets some of the light pass through to a second mirror that redirect light down to a focusing system. A compact camera has no mirror and therefore can only work off the sensor image. Some of the latest DSLRs can now switch to the same mode as compact cameras in order to allow you to see the composition on the rear LCD monitor but they then use the same focusing system. (My Nikon D300 in fact offers two focusing mechanisms for use when the rear display is showing the live image in addition to the standard focusing system when the mirror is in the way of the sensor.)
Some of the best glass (lenses) for modern Digital SLRs were made long ago, often before digital cameras existed. However, some non-professional older lenses or cheap lense do not allow quick focusing. A DSLR is ultimately limited by the quality of the glass that you put on it. Once you have got into a system, you can slowly invest in better glass that will last you years. Each manufacturer has its own system and third party manufacturers make for all of the popular systems.
Both my wife and I use Nikon, which is now the market leader in Europe. The other main competitor is Canon. Frankly, there is not much to tell them apart. I am on a Nikon D300 but you can now get the Nikon D90 which includes virtually all of the same capabilities, potentially slightly better overall performance (newer) and High Definition Video!! My wife has a Nikon D80 but has switched to using my "old" Nikon D200.
The other key players are Olympus, Pentax and Sony. Sony is a relatively recent entrant having acquired the business of Minolta a while back. (My first DSLR was a Pentax, called the *ist D and I had its film based predecessor). Sony is trying really really hard to be a big player in this market. The sensors that Nikon use are made by Sony (although to Nikon design).
Pentax is falling by the wayside (Jessops are ceasing to stock them for example).
Olympus have teamed up with a few others and headed off into a slightly different world firstly with the introduction of a new (smaller than usual for DSLR) sensor size called Four Thirds and more recently with the Micro Four Thirds system, which does away with the mirror I mentioned earlier (so technically, not a SLR – single lens reflex – system) that supports lens changing.
The resolution con
Take great care with regard to resolution. More is not necessarily better. The physical size of sensors in DSLRs is significantly greater than that of ALL compact digital cameras. Thus the amount of light that is captured and hence the quality of the image is greater from DSLRs. As resolution increases though for any given sensor size you are increasing the number of "light buckets" you have whilst decreasing their individual size, you are also increasing the amount of insensitive space between the buckets. This can simply increase the amount of noise (digital interference).
On a DSLR, 6Mb is actually fine for prints up to A4. 10Mb will happily give you good results at A3 and beyond with the right treatment. You will notice some DSLRs being referred to as "full frame" which means the sensor is around the same size as a 35mm negative (the "old" Canon 5D is a good full-frame DSLR, recently replaced by the 21 meg 5D mark 2, the Nikon D700 is another example of a full frame camera). In most reviews, the 12meg cameras come out better than the higher resolution cameras. Most DSLRs have an "APS-C" sized sensor which is roughly around 2/3 the size. This has an advantage in that a) the full diameter of older lenses is not used and it is at the edges that performance weakens and b) this effectively multiples the focal length of lenses so a 200mm lens is actually like a 300mm lens would be on a film camera (i.e. you "see" further). This size is still much bigger than that of compact camera sensors.
A place for both types of camera
There is no denying that compact digital cameras (and cameras on phones) are convenient. Indeed, I have recently invested in a new high-end digital compact camera (Panasonic Lumix DMC-LX3). However, once mastered, a DSLR gives much more reative capability, higher quality, and more flexibility.
I recommend a DSLR for a quality record
If you are serious about getting into photography and having a good record of your son and of any future offspring growing up, get a DSLR. You do not have to start at the top of the range (invest in glass – it lasts). Video is handy, but is often not as powerful or convenient a medium as a still image.