I assume everyone's philosophies on this will be a little different, but I'll give you mine!
First off, yes. You absolutely need a tripod. There are ways to get shots without one, like having a large aperture and high ISO, but they will not be the 'breath taking' photos you've seen. We almost always have a car with us at the world so I usually leave the tripod in the car and then sneak out sometime before the fireworks and grab it. I have carried it around all day and it's just not worth it to me. Setting up a tripod for Wishes! is pretty tricky. If you want a front and center position on Main St. you better be prepared to get there early and stand your ground. People have no respect for tripods. I've done it several times and my girlfriend and I stand on either side of the tripod and it still gets run into, kicked, tripped over, etc. Heck I've been in a group of photographers with 4 other tripods and we STILL got ran into! And the 4th will be super busy so it will be even worse. There are other places to set up that won't be so crazy but they are off-center and offer a different view. Good and bad I suppose.
The type of lens depends on the type of shot you want. If you want to get the full view of the show you will need a wider lens. If you want a tighter shot with maybe just the castle spire and bursts behind it then you will need a longer zoom lens. On the 4th they generally have perimeter bursts which come from Tomorrowland and Adventureland giving you a 180-degree show. To get all of this you will need a fisheye.
Shooting fireworks is probably the most rewarding type of photography for me. I've shot Disney fireworks shows plenty of times and I still get excited when I get a really good shot. To me there seems to be a lot of luck involved, more luck than skill. People will tell you to watch videos of Wishes to learn when the music queues are which can help a little, but just being there shooting is the best practice you can get. For me, I use a cheap wired remote. I think it was $3 on Ebay. I used to use a wireless one but I had the battery die in the middle of the show once and gave up on that! This way you aren't physically touching the camera, which can cause it to shake even on a tripod. I also shoot in bulb mode now. For a while I was just doing times exposures, but bulb mode is so much better. It gives you more freedom. Typically my shots are ISO 100, f/16-18, and a shutter speed around 20 seconds. Hopefully that helps a little!