1. I'll run with any world so long as there is a good supply or wood and water nearby. Everything else can be found everywhere, unless you need something biome-specific, like snow or cacti, the latter of which actually has some practical use (unless you're playing on Peaceful, in which case they're not used for much. As long as you have wood and water, you can make anything work.
2. I have a pretty good memory for that king of thing, so unless it's an absolutely ''massive'' cave system (and I've only come across one that qualifies as such in my book), I don't bother with markers. In any case, torches make pretty good landmarks if you get lost, above or below ground. You just have to make sure to place them in unique patterns in a cave.
3. I'll generally build a storage facility/crafting area, which has a workbench, several furnaces, and all the chests in which I store materials. Of course, in this game, the only reasons to have living quarters are aesthetic. I have my tower that I've built, but I spend very little time there unless I need to go to the roof and survey my domain.
4.