Hannibal should be fine. He does have an early UU that makes an aspect of the game easier, dealing with spear/axe/sword barbs without metal, but that's a very minor thing compared to something like being able to roll over half the world with Immortals. Especially on a relatively low difficulty.
Huts can be very unbalancing, since you can get something like Bronze Working -> Iron Working for free on T10 or something crazy like that while your neighbour gets a small sum of gold and a map. They become more and more favorable for the AIs as the difficulty increases, as well, since later on AIs start with a free Scout, which will never trigger a barb attack, and later still AIs will start with two free scouts so they'll eat up all the huts quickly and leave nothing for the player. Events aren't as bad, but they do require a slightly adjusted playstyle and there are a few events that are potential game changers. To name one example getting the event that spawns I believe 6-8 barbs right outside your borders out of nowhere is pretty bad, especially if you happen to trigger that event and you're next to whoever build Great Wall.
Tech Trading should be on, as having it off shuts down a large amount of diplomacy options and those are very important to learn. Dealing with having Shaka as a neighbour, for instance, is much harder without tech trading than with it, since you've got a lot less options.
I'd also recommend playing on Noble, it's a really easy difficulty to play on if you're at all familiar with the game's mechanics, and rest assured that the regulars here who play on Deity are very familiar with the game's mechanics.
Simple reason, you want yourself and the AI being equal.
