I realize that "we" have given the impression that you have to spend a lot to start competition.
That's not true. You will have to spend some but you can do it on the cheap.
Assuming you have a vehicle to haul the stuff and/or a trailer:
At least one canopy. A 10x10 will get you started. Even a $35 lightweight canopy will get the job done (two are nice to give you cover for your prep and a place to put "stuff".
I'd recommend at least two tables. One six footer (two is nice) and one card table will give you a place for prep and cleanup. Of course, another would be nice but you can certainly get by with two.
Three or four bus tubs. I like the heavy grey tubs from Sam's because the are large enough and deep enough to use for most of your pans, utensils, etc. And, they can be used for food prep, too.
Coolers - as soon as you can get a couple of 120 quart coolers. They get heavy but you can put 80-100 pounds of ice or all your meat with ice in one cooler. Another is great for "coolering" the meat. I've got 2 120 quart, 2 70 quart, and one 50 quart cooler that go out to every event. You can certainly do it with less. I now use one or two that are emplty to carry my seasoning stuff (sauces, rubs, sugar, juice, etc. etc.)
The goal is to get down to what you really need. I can pack all this in my Explorer and my "fire box" stuff (chimneys, lighters, extension cords, etc.) goes on the cooker trailer. I have also strapped one of the 120 quart coolers to the tongue of the trailer.
A source of hot water is essential. I use my turkey fryer. I always have the propane available for the cooker burner to pre-heat the chamber while the charcoal is getting ready. I usually take my short "fish fry" pan for hot water but last event I tood the 26 qt. turkey pot and it was nice to have the bigger pot - not necessary but nice. The Coleman portable hot water heater is definately an option and it can be fired from disposable propane bottles or, with adapter, the 20# propane tank. It can also be hooked to a water hose (if available) for continuous water - it comes with a 5 gallon portable water container.
Fire extinguisher! Make sure you have a good extinguisher - some events really check. One from Sam's or a pair of the smaller ones will be fine.
You cooker(s). We were finally able, at Dillard, to go with one cooker. Fortunately, mine has two seperate cook areas and we had space to cook and then hold the meat at different temps. After going out with 2-3 cookers in the past having the one was really nice. Don't get me wrong - a Bandera will work fine and if you team it with a WSM or even a kettle you can certainly be competitive. It's just that keeping track of what's going on with 2 or 3 or more cookers is stressful - not to mention the space required to carry multiple cookers.
Carry boxes - get at least a couple of Rubbermaid (or other brand) boxes for your "kitchen" stuff. I use to use a three drawer plastic set with the stand - one drawer had dry spices, one had the wet stuff, etc. This stuff will evolve after you do a couple of cook offs. They key is to KNOW where your stuff is.
This stuff is off the top of my head and I'm sure others will chime in with suggestions.
Also, and in my opinion it's a biggie, get used to cleaning EVERYTHING as your packing up to leave. Getting home with a couple of hours of scrubbing, wiping, etc. is a real drag. After Dillard and a 12 hour drive home it only took me about an hour to unload the stuff, put the cooker up, etc. That included emptying the meat cooler and cleaning and drying the stuff.
In spite of your best efforts the first couple of outings will make you think you're doing a remake of the Beverly Hillbillies!