I, too, have 3 boys that are involved in tee-ball and competitive rec league baseball as well as an active 4 year old. I outgrew my 3.2 2x zoom camera and was in the market for a new one. I researched for months and narrowed my choices down to an HP Photosmart 945xi and the Kodak Easyshare DX7590 5mp 10x Optical zoom camera. My family surprised me with the Kodak Easyshare DX7590 for Mother's Day. The camera arrived a week after Mother's day and so far I have taken 550 photos! This camera has everything I wanted and more. I would consider myself an experienced photographer, but not an expert just yet. There are many features that I like about this camera such as the camera dock - very handy not to have to fiddle around with a cable to transfer and charge the battery, just pop the camera on the base that stays connected to my USB port on my PC and if I want to download my photos, push a button and it downloads them to my PC. I like the rechargeable battery - I took 100 photos at a concert at night and the battery still had a charge left at the end of the concert. The zoom is amazing. I was able to zoom in on my son in center field from the 3rd baseline, between the openings of the chain link fence - it looks like he was posing right in front of me. This camera has MANY different settings - on the sports (action) setting, I was able to capture my son hitting the baseball and I caught the ball flying off the bat very clear! It has many presets for indoor parties, outdoor night shots (took a nice pix of the moon through the trees with a purple haze using a tripod), pix in snow, pix on the beach, and more that I have not used yet. The 2" LCD screen is very nice, the silent shutter is a nice plus, especially in places where shutter noise is disruptive (church, meetings, etc.). This camera also has has video capabilites that is limited only by the size of the SD card (buy a high-speed one if you want to do video). This camera also has an expensive 10x optical lens that is grooved to accept a collar so you can add other lenses and filters. The Easyshare software is nice, but be aware that to print photos from it, you must have Windows XP, it does not support Windows 2000 Pro so I must use my laptop to print photos.
My camera came from Buy.com and it retailed for $399. It was purchased through a friend at Yub.com, so we saved $4.00 and our friend earned 400 points. Kodak had a $50 mail-in rebate that came 2 weeks after sending it in, and 10 days after receiving the camera, Buy.com sent an electronic certificate for $10 worth of prints from Ofoto.com. I had never used Ofoto until I received the certificate and I was very impressed with the quality and clarity of the prints. I was able to add a sports border to my boys' baseball pix that make it look like a baseball card. They also have other borders available. The pix came in 3 days. Dell.com (Home Office store) has this camera on sale right now for $339 with free shipping. Kodak does not have the $50 mail-in rebate right now, but if you are not in a hurry to purchase one, keep an eye on their site because they do rotate this rebate, I have seen it several different times.
One more piece of advice, avoid A&M photoworld, BuyDig, and FotoConnection. They offer the lowest prices, but then they have to "verify" your order or state that you entered you credit card number wrong and call you with a high pressure sales pitch. If you don't bite, then they tell you that your camera only comes with a 15 minute battery which is a crock. If you still don't bite, they apologize and tell you the camera is in such high demand that it is on backorder for 2-4 weeks. In 2-4 weeks, you'll get another e-mail telling you that the camera is still on backorder. This is the classic "bait and switch." I tried to buy my camera from these 3 companies and got the same routine and after checking further into them, I found they were all based in Brooklyn, NY, probably all the same company with various websites. I was able to cancel my orders with these companies, but only after they became very rude and yelled at me over the phone. I calmly told them to cancel my order immediately or I was taking legal action and reporting them to the Better Business Bureau and hung up on them.
I hope this helps, good luck on your quest for a new digital camera.