Need help with photography/video?

I'm a relative newcomer to digital photography and video. As usual, I want more than I have-- taking action photos with my Canon Sureshot 1200 has been pretty frustrating in anything other than pure sunlight, regardless of playing with the settings. I don't know if I messed something up, or if this is typical, but I suspect it's typical.

I am wondering if, instead of upgrading to a better digital camera, I would be better off purchasing a digital camcorder and then doing captures in order to get nice quality photos? How does the price range compare? In particular, I'm unhappy with the lag time on the stills I try to take with my camera-- it's pretty much impossible to use photography for any action pics. They either blur, or it takes the photo long after I want it to, or both. I know there is a delay on digital cameras-- I'm just not convinced I can solve that when taking football photos and such. Hence my question:

Can I find a camcorder that would allow me to capture stills that would be equal in quality to an actual digital photo? Or am I going to be looking at thousands of dollars for what I want to do?

Any and all suggestions are welcome, and thanks in advance for putting up with what I know is a pretty entry level question.