Again I am going to agree with Pesto here the Nikon really is the way to go, if you are planning on spending money on a camera go to a full DSLR don't sell yourself short. The D50 is a great camera for a beginner and the D70 has a little bit more advanced features. Like was said it's you who is going to be using the camera so you must be the one to make the decision but man I would hate to not see you go with a good DSLR because the price is just awesome!

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I say go for the DSLR too. I bought a sony point and shoot and 1, yes ONE month later bought the canon 20D because the sony was not what I was looking for LOL. Definally go in to a camera shop and feel them out. I think you will really like the DSLR's.

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Check out the new Nikon D-40. Just came out. If you buy lenses for it, when you graduate to a more expensive Nikon down the road, you can always use the same lenses again.

D40 is nice.. just keep in mind that you cannot use older nikon lenses for this camera.. only specially made digital lenses. They will work on other nikons.. but it kinda closes down the used market to you. While the D40 is a nice step up from P&S and is a nicely featured D40.. if you can find a cheaply priced D50 or a used D50.. I'd go that route instead.

I read that about the D40 too, I guess I've been thinking if I go that route/brand the D50 is the likely option. I went to look at a 2nd hand Canon EOS 300 last weekend - the guy had put some russian firmware on it to unlock some extra functionality, anyone know anything about that???

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oohhh.. underground unlocked cameras! Nice!! I know that some functionality in Canon cameras are added to the software embedded on the chip but locked in a fashion so the functions are not available. This way, they use the same chip in say their mid-entry model and next step up model. Some aspiring hackers find ways to unlock the functionality and voila.. a better camera for a lower price.

I bought a new camera a couple of months ago. I was really on a tight budget, but needed one for a big trip. I used to have a very lightweight Kodak P&S that was horrible (never go there again). My budget didn't even come close to go DSLR, but I did want more room to experiment with manual settings, so that I can figure out if I could really handle that on a DSLR in the future. I found out that the newer Canon PowerShot models have that possibility. I ended up with a A610. It's only 5MP and 4x optical zoom, which is OK for me now. I loved the swivel screen, which I use a lot. I found it on internet for about $250, which was my whole budget. For a little more you can go up to a bunch more MP and optical zoom on the newer models and you can go all manual on all of them.
For my A610 I can also buy a few extra lenses, I'm not sure if that also goes for the newer models. I now figured out that I probably won't get the extra lenses, I figure that if I can save up $200-$250 for a lense, I'd rather save up some more and go DSLR after all. I'm not in a hurry anymore and in the meantime I can keep experimenting with my A610.
I'm not sure if this is what you are looking for, but thought I'd let you know anyway. Good luck on making your choice!

OK, I went back to read your original post and figured out I left out a bit of the story. The A610 also has a burst mode so you can take a bunch of pictures right after each other. But I'm also amazed at how quickly this camera writes the picture onto the memory card, so you can quickly take the next one. I generally use a high speed memory card, but I must say that when I have an older, regular speed card in there, I hardly notice the difference.
For the quick pictures of the kids, the auto mode works fine. And there are also a few preset modes, to help with good pictures of the kids, when there is little time (especially while you are still working on your manual skills).