Welcome to DCI!
For that sort of money, you're well into digital SLR territory. The good news is that modern DSLRs can automate just about any area of their operation, to the point where they can be made to basically be big point n' shoots.
The best way to approach this is probably to determine what you need in a lens, select a relevant lens from one of the manufacturers and then pick a camera body to fit that lens.
In order to figure out what sort of focal length lens you need, there are some gaps that really need to be filled in. I'll give some examples of focal length and state my assumptions, but it'll be up to you to determine whether they make sense.
The first assumption is on the size of the subject. I figure that a horse that's 15 hands and a rider might be a total of 8 feet or so tall on average, so I'll work with that.
The next assumption is how much of the frame should be filled with the subject. I usually assum that the frame will be three quarters filled in height, but you might come back and say otherwise. For any given subject, filling more of the frame requires a longer focal length, and filling less is an easy way to back off that requirement.
Finally, we need to know roughly how far you'll be from your subject. Obviously, the further you go from the subject, the more powerful the lens has to be as a result.
I have no idea how far away you're going to be, but given the above two assumptions I can list a bunch of distances and the required focal lengths (in 35mm terms):
50 feet away: 150mm focal length required
100 feet away: 300mm focal length required
150 feet away: 450mm focal length required
200 feet away: 600mm focal length required
Those numbers are calculated with the focal length calculator here:
http://www.cambridgeincolour.com/tu...mera-lenses.htm
The good news is that most digital SLRs have a smaller frame than 35mm film, and thus have a "crop factor" that works in your favour for long distances. For example, Nikon digital SLRs have a crop factor of 1.5, meaning that for equivalent results to a 35mm frame, they require a focal length of 1.5 times less. The 150, 300, 450 and 600mm examples above then become 100, 200, 300 and 400mm as marked on the lens to reach those distances.
So, which lens do you need? Well, knowing what sort of focal length you need would help. Also, you didn't mention whether the competitions are held outdoors or inside in some sort of arena. The former is definitely more desirable as there's a lot more light available.
One other thing to think about is whether you're looking for an optically stabilised lens. With these, as the lens senses the camera moving during a shot, it moes one group within the lens to counteract things, which results in less blur due to shake. This can't cure all ills, but does have a very noticeable effect, especially at long focal lengths.
The downside is that these lenses always cost more.
Anyway, assuming you're outdoors, then there are a few fairly inexpensive options available. If you don't have to go any higher than 200mm, then Nikon has a new
55-200mm lens with their Vibration reduction feature, which is their name for optical image stabilisation. That runs for about $250 or so (using B&H prices as a benchmark) and is probably a better deal than any non-stabilised 200mm lens.
The other alternative for Nikon is their 18-200mm VR lens. This is stabilised and has good wide range. It's not cheap ($750 or more) and it's really difficult to find anywhere that has one in stock (good luck), but a lot of people buy this lens and then never take it off their camera.
At 300mm, there are a bunch of lenses from several manufacturers (including the third party guys like Sigma, Tamron, etc.) currently on the market.
There are several without any form of stabilisation, but they do vary widely in quality. For a cheapo lens in this range, I would probably go with
Nikon's 70-300mm G partly because it's so cheap ($140 or so new) and partly because supposedly it's a fair bit better than Sigma's offering, and a whole load better than Canon's 75-300mm offerings. There are potential compatibility problems, though - more on that in a bit.
Given your budget, there are basically two 300mm stabilised lenses on the market that are available. Both Canon and Nikon make lenses in the 70-300mm range with each manufacturer's stabilisation systems:
http://www.nikonusa.com/template.ph...&productNr=2161
http://www.usa.canon.com/consumer/c...0&modelid=11922
The Canon has a little bit larger aperture at the 70mm end and costs $550 or so, whereas the Nikon is $480. Both are supposed to be good lenses and from what I've read, there's not much to choose between the two.
At that sort of price, there is also a Canon 70-200mm L series lens. It doesn't have image stabilisation but does have a constant f/4 aperture over its whole zoom range, which is a whole stop faster than the f/5.6 of the two 300mm lenses at their long end. I'm betting that the longer focal length plus image stabilisation is a better deal for that price, though.
Oh, and even if you determine that 200mm might be the maximum focal length you might need right now, it might be worth considering tthe extra cost of the 300mm lenses. They're a bit more flexible, but more importantly at 200mm, they're not at the limit of their range and will perform better than a cheap 200mm at its limit.
Assuming one of the latter 300mm lenses met your needs, you'd have about $1000 left (give or take) to spend on a body. If you went with Canon, then that would mean either an XT ($570 with the kit 18-55mm lens) or an XTi ($765). The resolution difference (8 vs. 10 MP) is completely irrelevant, but the added features on the XTi (bigger & better screen, sensor dust removal system, bigger image buffer, better autofocus system, various firmware tweaks for usability improvement) may well make it worthwhile.
In the Nikon camp, there are 3 contenders. The Nikon D40 ($525) is Nikon's current entry-level DSLR, and the D40X ($700) is its slightly revised bigger brother. The difference between these really isn't all that clear-cut - the D40X adds a 10 Megapixel sensor over the 6MP of the D40, and that's really about it. A lot of people questioned the point of the D40X - the resolution jump is more significant than the difference between the Canon XT/XTi, but a lot of people don't feel that $175 is really worth that.
The D40 and D40X both share another limitation where lenses are concerned. Nikon has traditionally driven the autofocus of some of their lenses with a motor in the camera body, which turns a screw in the lens to change the lens focus. This is completely missing in these cameras, so they are restricted to AF-S lenses (at least for autofocus) where the focusing motor is internal to the lens and is driven electrically.
Nikon reckons that most people buying the D40 would be newcomers to digital SLRs and wouldn't be interested in some of these lenses. The camera will still work with these non AF-S lenses, but they can only be manually focused.
The D40 will work just fine with the 70-300mm VR lens above. It's an AF-S lens and will be just fine on a D40. However, the non-VR 70-300mm G isn't an AF-S lens, so unless you want to only focus manually, that's not an option on the D40.
Don't get me wrong - the D40 is a really great little camera. So long as you understand the implcations of its lens compatibility and you don't mind that, it (or the D40X) might well be a great fit for your needs, especially as its low price point gives you that bit more to spend on a really good lens (which also costs a bit less than Canon's).
If these lenses are interesting to you, then short of manually focusing, the other option (when buying new) is the Nikon D80 ($1000). This is a slightly bigger camera that retains the focus motor and is compatible with all these lenses. It also has improvements in its autofocusing ability, image buffer size, usability and general build quality.
Personally, I just received a D80 last week, and I'm loving it. This is my first foray into digital SLRs, and so far I haven't been disappointed. It was the lens thing that did it for me - I wanted to get a
cheap 50mm f/1.8 prime lens and didn't want to be stuck with manual focus. I felt that overall Nikon's lens selection was a better fit for my needs in the long term. At some point in the future, I'll either pick up the 70-300mm G or the VR version, but not right now.
Even my wife was impressed by the first few pics I took of my daughter, so it's already been worth it:
http://www.flickr.com/photos/691781...57600438245580/
It may not look like much, but that little 50mm lens is an absolute gem. It's completely divorced from your needs, but there you go.
Anyway, unless you really feel strongly about those Nikon AF lenses, I'd say you should stick with the D40 or the Canon XTi for now. Even with the larger $500 or so outlay for a long zoom, that still gives you some (or plenty in the case of the D40) cash left to either sit in your wallet or to pay for a bag, filters, mono/tripod, memory cards, etc.