Assuming those southern california sports teams are broadcasting their games on regular (cable) TV channels, then you could certainly sling them with a Slingbox located in California for viewing in Florida or anywhere else in Intenet land.
As for viewing the output from your video cameras, I suppose you could put the output of those cameras into a slingbox as well. But I wonder if that would be overkill. My stepson just installed over the weekend a set of video cameras around his house (in Northern California), and he has their video and still photos being sent to his iPhone through some app that came with the cameras. He didn't go into the details with me (but did show me the images on his iPhone) but he's no computer networking guru, so I would assume that it was a very simple process to set up. And, because he is somewhat "value conscious" (a.k.a. cheap), I don't expect he paid a lot for the setup. I think he purchased everything online through his Costco account.