I think for what you shoot I would hands down go for the 40D.
The original 1Ds, while still a great camera, just can't keep up with today's cameras. It has killer AF sure, but you're limited to 3FPS, it's higher ISO is nowhere near the quality of even the 40D, let alone the original 5D. Plus you will not get live view (if that matters) and a much smaller, less sharp LCD (if that matters.
I've owned the original 1Ds and it was a brilliant studio camera, and awesome for landscapes and travel photography. I would not recommend it for the application you've mentioned.
Next, the original 5D. Great camera, seriously, it's just a bargain for the image quality you get. But it is S L O W. I've tried shooting sports with it and it's a nightmare. I bought the original 5D when it came out and it was companion (and eventual replacement to) my 1Ds. It is most excellent for portraiture and landscape photography, but not sports. Slow AF, and Slow FPS.
If you could be so lucky to find a used 1DmkII for your budget it would be the best bang for the buck for sure! I traded my 1Ds for a 1DmkII and that camera is just BLAZINGLY fast. But it's unlikely you would find one for that cheap that wasn't beat to all hell.
I'm currently shooting with a 5DmkII (gripped) and a 40D (gripped) I just picked up the 40D w/ the battery grip for $750 (it had about 7.5k on the shutter) It's been excellent for high school volleyball, and I'm going to shoot a concert with it tonight (along with my 5D)
I think for the value, the 40D would be a worthwhile upgrade for you. You can get it for a reasonable price, and it's suitable to handle most any type of photography.