If you can get both, then by all means get both. They are not an essential part of upkeep, but they are great at helping create an autonomous system. Excellent if you are busy with work, school, family, etc. If you have the time though, nothing beats a mindful eye and a hand-bottle, haha. I use 3 Vicks humidifiers for my cham-room and an Aquazamp system to run all my cages. I still use a hand-bottle though. One thing I should mention about humidity levels is that you should shut-off the humidifier every so often for maintenance cleaning and to let the enclosures dry out. Letting humidity levels drop every once in a while is not a bad thing. If you do get a humidifier that is not a reptile-name brand, I advise to go with a warm mist vaporizer over an ultrasonic. The reason being is that although mist is less visible on a vaporizer, it is both more reliable and does not promote mold-growth. Ultrasonics, while being cool looking, are sometimes unreliable, difficult to clean (not all of them), and get moldy quick.
When it comes to misting systems, Aquazamp and Mistking are both top-notch. DIY systems can be made with any booster pump. Good luck pal.
Almost forgot to answer your specifics...
1. Some chameleons are afraid, some are not. Most will adapt and get tolerant of misting.
2. If you are unsure about how much to water, get a tray and overdo it a little. It is best to err on the side of more not less, when it comes to watering. If you are confident in your observation skills, and the enclosure has enough foliage, It is possible to not need a tray for watering. I do not use trays, from time to time I do drip some water, but never enough to soak my floors.
3. The best store-bought rain system hands-down is made by Aquazamp. Summoner12 is a longtime member of this forum and a very knowledgeable cham-keeper.
4. A rain or mist-system is much more useful than a humidifier. If you can afford only one, then get a mist-system. Remember though, they are both luxuries, and not a mandatory item. They are very helpful though.
5. I do not know where to get a Quad at the moment, but Backwater Reptiles gets them from time to time. They mostly have wild-caught and although they do not have the best reputation, they really are just middle-men and cannot be blamed too much for cham conditions. Backwater does have good deals from time to time. There are plenty of options though, expos, other members, and local ads. You would be surprised to see how lucky you can get sometimes with local ads.