I think I can answer a few questions here.
You can buy a heavy duty extension cord with a gfi built in at Home Depot.
That's what I use. It's nice because it keeps the plug and wall outlet far away from the tank area.
First of all, I would buy one that actually lists how many amps it can handle (15 is normal). Obviously you wouldn't want anything higher since the wall outlet is rated for 20amps which will trip the breaker. If it doesn't have an amperage rating, then I wouldn't assume! It could be meant just for light duty like running a desk lamp or something. Sometimes you will see ones that say 300V. Note that this does not specify how much amps it can handle, just max voltage.
Waiting for the cord to get hot is one way or you could do your own safety calculation.
Let me stress this is my rough common sense calculation. If something horrible happens remember that I'm NO expert.
I don't mean to sound condescending, but you can calculate how many amps you are drawing with the simple OHM's law formula P=IV
Power in watts, I is current in amps and V is voltage in volts.
Now if you are running two 250W MH ballasts that's 500W. So 500W/110V is roughly 5amps. You are safely within range using an extension cord rated at 15amps.
However if you put a pump, and two 400W ballasts on it, then you're getting closer to the limit:
1000W/110V ~ 10Amps.
Watch out cause a normal chiller will draw close to 1000W when it switches on!
All of your devices will say somewhere on them how much power they draw. Of course they aren't always drawing the max amount of power so who knows what's actually happening. And of course if there is some kind of short then they will start to draw a large amount so hopefully the gfi will trip or the built in breaker in your outlet strip will trip before the socket starts to fry.
Arc faults are rare in general, but if salt creep gets on the outlet they are almost sure to occur.