To add to what Mark said, the cameras he suggested both have viewfinders. Many feel that a viewfinder held to the eye is much better for tracking action than trying to do it with the more common LCD screen. The FZ 150 may be the least expensive current camcorder that has a viewfinder, shoots in 1080p and gets significantly good reviews for both photos and video.
You didn't ask, but since you are new here, the reason the 1080p is important is that ithere are 60 full frames taken in each second. That makes action flow smoothly on play back. Additionally, there is software that can make a pretty good snapshot from each of those frames. For example, I have a favorite ink jet print on my wall that has my (drop dead gorgeous) 10 year old granddaughter swinging a bat at a ball about 1/60th of a second before she smacks it. The ball, six inches from her bat, is a little blurred but she is frozen with an amazing look of determination. The video is good too!
Another reason for the 1080p is that, with some editing software, you can get some "slow motion" from it. I used an even cheaper camera, the Sony HX9V, to shoot my brother shooting a replica of a 1776 muzzle loading rifle. It allowed me to spread the actual firing over a few seconds of playback. My brother was ecstatic when I sent him a YouTube clip. (The current version of the HX9V is an HX20V and it does not have a viewfinder.)
To summarize, you don't need to spend "$$thousands" for good sports video. You can spend that if you want, but spending a few to several $$hundred will get you a camera that takes wonderful sports video -- as long as you pick one that included "1080p60" in the specs.