I was considering a SLR because I was told the bigger the lense the better the picture and the label advertised quick shutter speed and a good amount of zoom. The main problems I am having with p&s is 1) zoom capabilities 2) I hate the slow shutter speeds, everyone usually moves between the time the button is pushed and when the picture is actually taken 3) I take used to a lot of pictures at night especially on vacation, but they never turn out right. I don't even try fireworks or the light parades now. 4) If I use any function other than automatic, the pictures are blurry. DS plays sports and I would love to use the sports option that takes a bunch of pictures in a row, but they still all come out blurry. 5) I do like to enlarge a lot of pictures.
The model I am looking at now is $599. I have been saving for a camera so that is do-able, will a basic SLR do the job without add-ons, at least in the beginning?
The basic lens ("kit lens") is not a very long focal length lens. Comparing it back to a p&s, it is like a 3x zoom, but it starts wider, so if you are looking for a decent range of zoom, you might be better off with a bridge camera or spending more if you want to stay with a Nikon. You would be looking to either upgrade to the 18-135mm kit package or adding a second lens around the 50-200mm range. Either way, it would probably be over $100 more. If you would be willing to give Pentax a look, they have a great deal on the K100D, 18-55mm, and 50-200mm all together for around $600 due to a $150 rebate when you buy all together at the same time. It is good until the end of the month.
For the shutter speed, I am pretty sure you are talking about the delay from pressing the button to it actually taking the shot. That is the best with a DSLR, but the newer p&s models have come a long way, so don't count them out just for that.
For low light, it seems like your bad shots always involved motion. If so, you should also look into a wide aperture lens. The 50mm models seem to be the most popular due to their usually low prices. The Nikon, Canon, and Pentax models can be found for less than $200. (take note that the 50mm Nikon will only be a manual focus on the D40 and D40x) Without one of these, a DSLR will be better than a p&s due to having a usable ISO 1600, but it might still leave you wanting more. For low light shots without motion (including fireworks) it is easier. Get a decent tripod and a remote shutter release. That goes for any camera. If no shutter release is available, a camera with a 2 second shutter delay will also work, but timing can get difficult.
Also for low light, take note that the Pentax, Sony, Samsung, and newest Olympus models have IS built in to the body, so it will work with every lens. The IS built in to the lens is technically a little better, but at a huge price difference.
If you decide to go for a DSLR, it is a good idea to get out of the automatic zones. The depth of field is much more controllable on a DSLR, but when you leave that up to the camera, sometimes it makes mistakes and you will miss your old p&s. A very good book on learning more is Bryan Peterson's
Understanding Exposure.
If you plan on using the burst mode often, then you might need to lean more towards the Nikon or Canon in the entry level range. The Pentax is limited to three RAW shots or five JPG shots in a row before having to clear the buffer. The entry level C&N are not much better than that, but are still better. I personally hardly ever use that feature, but I do not do much action photography.
You will have more to work with when enlarging with a DSLR and you should also take advantage of RAW. As I mentioned before, a 6MP DSLR will give you more to work with than a 10MP p&s. It is because the image sensor of a DSLR is so much larger.
Good luck. If you go with a DSLR, you will likely be happy with it no matter what brand you pick. They are all good.
Kevin