Hi Maurine and welcome to the Q&A Board,
No, you no longer have to get a SLR type digital camera for rapid fire. Most of the digital cameras that have come onto market this past year are much improved, with little or no lag time and can fire rapidly (though rapid fire using a flash still leaves something to be desired).
IMHO, there is still no "best" digital camera, no matter what price range you're looking at. What's important is to find one that has the main features you want at the price you can afford.
Here is a listing of some well-rated cameras, many that have come on the market this year:
http://www.digicamhelp.com/digital-camera-shop/index.htmHere is a chart that can help you decide the type of camera most suited for you photo-taking style.
http://www.digicamhelp.com/choosing-a-digital-camera/index.htm