To deal with distance (arenas) just get a quality telephoto lens to screw on the front. Sony makes (or made?) a great one for the tape era cameras. I still use it on my digital Canon (surprisingly the thread is the same size).
^ For criminy's sake get a decent plug in mic too though. I stopped buying Sony cameras (after over 20 years of loyal use) because they didn't make one you could plug a mic into (unless you wanted to drop $2K, which is totally unnecessary now).
My recommendation is a Canon Vixia. Real video camera (that can record hours at a time at true HD) with all the controls and the built in mic is actually up to most challenges (though I always plug a mic in).
I do still miss the magic Sony exposure wheel control, but I don't think they offer it themselves anymore. That was the best thing ever in the old days when the resolution and circuitry wasn't as good as it is now.