Though the word "caramelized" is associated with sweetness (it refers specifically to sugar browning, after all), you don't want to do this with so-called "sweet onions" such as Vidalias or Mauis. That's because those onions aren't actually sweeter than regular onions.
The so-called sweet onions actually just contain less of those sulfurous compounds than regular onions. This makes them taste sweeter when they're raw and they are splendid sliced onto sandwiches or into salads.
But they also contain less sugar than regular onions, and because those acrid sulfurous compounds pretty much go away when heated, sweet onions turn bland as water after cooking.
The bottom line is, regular brown storage onions will make better caramelized onions than pricey sweet onions. You can use red onions if you like -- they have sufficient bite -- but the end result won't be any better than with the brown ones, so why bother?
All those tears
It's irresponsible to write about a recipe that calls for slicing 5 pounds of onions without addressing the question of "How do you keep from crying?"
I wish that I had some kind of miracle cure, but after 30 years of chopping onions, I don't. Essentially, what makes you cry is those sulfuric compounds, and they're created whenever the onion's cell walls are broken.
There is no end to folkloric cures for this. Some people swear that holding a wooden spoon clenched between their teeth works. This isn't as silly as it sounds, because squinting can reduce the amount of those gases that gets in your eyes. Goggles are said to work for the same reason. But there is dispute among onion chemists (yes, there are such people!) as to whether it is your eyes that react to the chemicals or the lining of your sinuses -- so if you want to try this technique, better make it a full-face mask.
I've tried the wooden spoon trick and not only did it not work for me, it made me feel even sillier than usual -- a big spoon in my mouth and tears running down my face. Your mileage may vary.
The only trick I've found that works isn't really a trick -- keep your knives really sharp and it will minimize the amount of cell damage and reduce the amount of sulfuric compounds released. In essence, you'll be slicing through a thin band of cells rather than crushing a wide one.
Other than that, the best thing is to do what I do when I'm standing there sobbing over a cutting board full of onions -- remember that tears are temporary, but the joy of having a jar of caramelized onions in the fridge lasts a long time.