Look into a Nikon D40 bundled with the 18-135 lens. This range should be good for the vantage point you have described. You can get them for $720 at B&H Photo and add a 1 or 2 GB card and come in well under your budget.
The D40 will give you a burst speed of 2.5 frames per second. This is not really a blazing rate, but for the money, you are not going to get 5-8 fps that really serious sports cameras provide. The good news is that Nikon claims you can take an unlimited number of frames as the buffer will be able to dump to the card faster than you can load it up with images. Be sure to get a decent speed card, though. I'd get a Sandisk Extreme III or Lexar "Professional" 133X and I'd get at least 2 GB if you plan on doing a lot of burst mode shooting.
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Fhotoace has suggested a longer lens. Since he makes his living doing this, please give his answer all due consideration. I just thought you were within reasonably close range, as if you were NOT in a major league ball park and the 135 (202 equiv.) would be adequate. Your budget is actually my main consideration and you'll have to do the best you can with what you can afford. I have a 70-300 lens that would be great, but there are two problems. One: It seems that you can ONLY buy the D40 with a lens and not the body alone, so you have to choose the best for your needs. Two: If you wanted to add the 70-300 lens to the basic kit, even if you went for the mid-level, non-VR lens, it would add $330 to your cost. Combine this with the cheaper 18-55 kit and you'd spend closer to $900 by the time you bought a decent card. If you can do this, it's worth considering. I think you might try the 18-135 for one season and save your money for an additional lens so you can get the VR lens (a real help with those longer focal lengths) for more like $500...
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Here's my stock recommendation for the D40. There is some duplication here with the material above that I wrote specifically for you, so just skip any parts that sound familiar.
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Nikon D40
The Nikon D40 is a great little camera, very easy to use and quite reasonably priced. It has a few "consumer friendly" totally automatic modes that make it very easy to use - including a "Child Photo" mode - but still offers total photographic control when you are ready to take charge. It will get you in the Nikon family which is a great place to be. If you buy accessories and lenses, you will be able to use everything on any Nikon that you might upgrade to later on.
Check out Nikon's "Picturetown" promotion, where they handed out 200 D40's in Georgetown, SC. http://www.stunningnikon.com/picturetown/
Here are a few reviews, in case you have not read them yet. Be sure to note that they are several pages long and some of the reviews also have some sample images that you can look at.
http://www.dpreview.com/reviews/nikond40/
http://www.steves-digicams.com/2007_reviews/nikon_d40.html
http://www.popphoto.com/cameras/3756/camera-test-nikon-d40.html
http://www.kenrockwell.com/nikon/d40/d40-recommendations.htm
I hate to see people slam the camera because it can't autofocus with older Nikon lenses. It is true that there is a "slight problem" with older Nikon lenses not autofocusing on the D40, but if you do not own a bag full of older lenses, it is not going to be a problem. It is barely a problem anyhow. If you check www.nikonusa.com for "AF-S" lenses, which are ALL 100% compatible with the D40, you will find 23 lenses, including 7 "VR" (vibration Reduction) lenses and one true macro lens with "VR". There are another 25-plus lenses in the current catalog that provide all functions except autofocus as well as many (possibly dozens) "out of print" lenses that will work just as well. In addition, although these lens will not autofocus, most of them will still give focus confirmation. From the D40 manual: "If the lens has a maximum aperture of f/5.6 of faster, the viewfinder focus indicator can be used to confirm whether the portion of the subject in the selected focus area is in focus. After positioning the subject in the active focus area, press the shutter release button halfway and rotate the lens focusing ring until the in-focus indicator is displayed." (See http://www.members.aol.com/swf08302/nikonafs.txt for a list of AF-S lenses or see http://www.nikonians.org/cgi-bin/dcforum/dcboard.cgi?az=read_count&om=16715&forum=DCForumID201 for even more...)
The D40 only has 3 autofocus zones arranged horizontally at the center, 9 o'clock and 3 o'clock positions. This might be considered a limitation, but realistically, most people will find this perfectly adequate, especially if you are moving up from a point and shoot with only a center zone.
There is no "Status LCD" on top of the camera, but Nikon chose to use the rear LCD for this information. This is actually a nice move, as the display is bigger than the top display and you aren't using the read LCD for anything BEFORE you take the picture anyway. This is not a step backwards and it actually makes sense to me.
You can get the D40 with the 18-55 kit lens at B&H Photo available through Yahoo! Shopping or at 1-800-622-4987) for $525 (June 2007). Add a Lexar Platinum (60X speed) card for $25 or 2 GB for $35. Or - get the D40 with 18-135 lens and 1 GB Lexar card for $750. This is a decent lens and it is very versatile. You will find it suitable for pretty much anything you want to do, other than really long telephoto shots. It will let you explore the range of focal lengths to decide where to start filling in your lens collection. If you don't want to buy any more lenses, this one will carry you through pretty much everything. B&H also have used D40's with the lens from $475.
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