While I can't make recommendations, I can help with the "which ones will autofocus?" question. Incidentally -- if you're looking at sports/cheerleading photography, then yes you definitely want autofocus. Manual focusing for sports or fast action is really not a viable option, unless you're extremely experienced (and even then, it's still a pain!)
If you're looking at Nikon-made lenses, any lenses labeled "AF-S" (NOT just "AF") will autofocus. Sometimes these are also called "SWM" (Silent Wave Motor), but "AF-S" will always be listed too.
If you're looking at Sigma-made lenses, look for "HSM" (HyperSonic Motor)
If you're looking at Tamron-made lenses, look for "BIM" (Built-In Motor)
Those are some of the most common. If I've forgotten any, I'm sure others will chip in too.
