I am a Professional Photographer and what you are asking for is impossible with the restrictions that you are imposing on yourself.
If you need help with a DSLR selection and lenses and how to do indoor sports photography, let me know.
My camera is a Panasonic DMC FZ28 it is already outdated but a great digital camera....
Sorry, you really need an SLR.
Get a basic SLR like one of the Canon Digital Rebels or the Nikon D3100 or D5000, then get a fast, short telephoto like an 85mm F1.8. Fast lenses and short shutter lag make the difference.
You don’t need to go high-end, but you do need a fast lens that lets in a lot of light. All the superzoom all in one cameras have very slow lenses at the long end of the zoom range. These don’t work for indoor sports.
My wife does photography professionally and loves her Canon 7D, but then you stated that you don’t want a digital camera, so that’s down the drain. (Also, the 7D is on the expensive side).
The best advice I would give you is get a really good flash. The problem with most indoor sports pictures is the delay in waiting for the right light conditions. We had a used Canon before the 7D, and we bought a good ($350) flash for indoor sports pictures. It made all the difference in the world.
As a side note, we were taking mainly Wrestling pictures where the action changes very quickly and you need a good flash to catch the action.
In short, if you go cheap, you get cheap results.
Wait for the Nikon 5100 DSLR. it should be out in a few months.
I agree you need an SLR although even the cheapest one out now will do. For a lens, try an 80-200mm f2.8 and one of the cheap 50mm f1.8 lenses. If you can afford it get the f1.4 model.
If money is tight, try one of the Tamron or Sigma models.
I guess one of the new EVF models such as Olympus which take interchangeable lenses would work too but I am not familiar with them.
I bought a Panasonic Lumix ZS7 last summer, 12megapixel resolution. It has, in 35mm equivalence terms, a 25-300mm zoom lens from Leica, some kinda image stabilization and will also take (some) HD video at the push of a single button. It’s also pretty small.
I love it !
You will eventually want a 18 - 200 lens as well.
Get a big one.
You’re welcome.
But the price of entry is pretty high.
My wife and I do a good bit of wildlife photography. We just went to Costa Rica and got shots of birds that the folks with the DSLR couldn't even get the camera ready.
As far as response time the newer P&S have great burst modes. You can snap off 2-10 shots in a second. That will help you get the shot better than trying to time it.
Her late \st camera is an Olympus with a 35X zoom lens. But her previous camera is a Lumix. I think it is a little better camera. So I would seriously look at this one:
http://www.amazon.com/Panasonic-DMC-FZ40-Digital-Stabilized-3-0-Inch/dp/B003WJR694/ref=pd_cp_p_1
At $300 it is less than the flash for some of the cameras listed above. If you try it and don't like it (for indoor sports) you will still find it a great all around camera and then you can look at plunking down the price of a decent motor scooter for one of the DSLRs they are talking about.
Sony
My late Father shot a lot of sports for newspapers back in the 1940s and ‘50s. He always used a 4X5 Speed Graphic.
Don’t worry about it.
Turn off the flash and kick up the ISO as high as you can and click away and have some fun.
The key is to plant yourself on the end line so you can be as close as possible to the action under the basket.
The next step up if you really want pro-level shots is pretty dramatic.
Here’s my usual load up when shooting sports.
2 x 1D MK III
1 x 5D
1 x 24-70 f/2.8
1 x 70-200 f/2.8IS
1 x 300 f/2.8IS if handholding
or
1 x 400 f/2.8IS if not.
5 x 32GB CF cards
1 x 580EX II flash
1 x Epson p5000
1 x monopod
All together this weighs about 60lbs. That’s why I don’t do football anymore. I’m too old to run up and down the field with 60lbs strapped on me. Give me a nice baseball game where I don’t have to move much.
Finally if I may make a suggestion. Want to try equipment out and not bust your budget so you can feed your child? Rent it.
Try www.borrowlenses.com. These guys are my friends and they have really good service.
It's nearly impossible to get a 1/300th sec. shutter speed in the lighting of a high school gym, football field, or track.
The only way to avoid soft pictures is by having a good enough lens and fast enough shutter speed to handle the conditions. Neither is cheap and the two together can be pretty costly.
Mostly it depends on how much softness you are willing to settle for.
I've noticed that many people are just hit or miss on photography and never understand the basic principles. They never get the full benefits of any camera they have.
what price range do you want to stay within?