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I've never entered the end in survival on Java edition. I am a bit worried because I am terrible at PvP, so probably pretty bad at PvE, too. This is my equipment. (I am not wearing a helmet because it would cover the eyes of my skin LOL. But really because I don't have a good one yet and might consider wearing a pumpkin.) Anyways, my armor and weapon enchantment are as follows:
Chestplate: Prot III, unbreaking III
Leggings: Prot III
Boots: Prot III, unbreaking III, FF III, depth strider III
Sword: Sharpness III, sweeping edge III, unbreaking III
Bow: Power IV, unbreaking III
I intend to use the speed potions throughout the fight and have a healing II ready at all times for when I'm below half health. The strength II's are for when the dragon comes to the nest and you can use melee.
You're pretty well setup, but I'd bring along two buckets of water for thinning out the endermen. The fight is already going to be long and slow, so why suffer through most of the not-attacking-the-dragon time having to deal with endermen?
Aside from obvious improvements (eg. bump all the protections up to 4 and the sword up to Sharp5, the pick up to Eff5),
an ender chest with spares of everything that will fit (& silk touch on at least one tool) [Accessing it may be difficult "under fire", but having a loaded ender chest may be the difference between difficult and no chance if you have some bad luck/make some mistakes.] infinty on the bow (mainly to free inventory from having to carry more than 1 stack of arrows) and carry a few stacks each of iron bars and ender pearls. (Also, I'd probably leave the empty bottles out and wait for dragon 2+ to collect dragon's breath.)
I'm assuming the stack in slot #7 is obsidian, if not this is good to carry for "ender blinds"
I'd also max out all the stacks (no extra cost to carrying a full 128 ladders.)
If you have the resources, golden apples stack well and can replace steak.
If you think the space is well spent, slime blocks (good for jumping down) and generic junk blocks (for bridging) are also useful.
Definitely don't go bare headed; my preference is a maxed out helm, but a pumpkin/carved pumpkin has its adherents.
You might consider not having Sweeping Edge on your sword; the dragon is all you want to hit, and endermen already get enough in the way.
Agree about the 2nd water bucket, and make an infinite source first thing (in case you need to replenish). [With Depth Strider3, you can use water as an area denial tool against endermen with comparatively little loss of speed.]
… good luck, and may you not need it. :>:
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.