Let's just say that while on a family vacation, I wanted to take a rod that I could cast out and leave in the surf while playing with the kiddos on the beach. How would you rig up your gear for such a scenario?

My first thought is to use a pyramid weight floating free above a swivel and flouro leader. Will this work or is there a better way?

Also, what are the chances of catching something for bait in the surf with a cast net? We are renting a house right on the beach and leaving to buy bait kind of defeats the purpose.

On the cast net, I'd say very good. I do better with a bigger net. It's been about timing and noticing the sign than about blindly throwing the net. Shin deep water is typically where I find Mullet. Cut the big ones. One well timed throw can set you up for a morning. We've used a Minnow seine with good results too.

They sell some terminal rigs for sharks and redfish. I have studied them before and then rolled my own if I have all the right components. I can't quite visualize how it goes together at the moment.

There are a bunch of rigs, ranging in complexity that will all work.

My favorite is close to what you described -- essentially a big carolina rig.

Hook ---> leader --> swivel -- mainline, as you described. Then on the mainline above the swivel you'll pin a second swivel so that it can slide down to the inline. From that drop a line to the weight. The "leader" and the line to the weight are the same length. The major advantage of this over what you described is less helicoptering on the cast, which costs distance.

You won't have much time to play after you cast out, lots of fish in the surf and you can catch bait in the surf with a cast net as stated above. Just take a break every so often and fish. Unless you are isolated (doubtful) you need to watch your gear and be sure others aren't getting ready to walk/swim into your line, beleave me many are clueless. If you are on the beach go before the kiddos get up then just mess around later.

I don't think you need a fluoro leader, but if you do just use a carolina rigged pyramid or bank sinker. If you're straight tying, tie a 2 foot long spider hitch into the line. Cut the loop where you have 2 tag ends. One end about 8" long. Tie a snap swivel on that end and attach the sinker (so you can change out depending on tides without having to re-tie). On the long tag end tie your hook.

I usually use double drop rigs and spider weights.

Exactly what kqt said