Assume you used the first two ASIs to maximize the intelligence for a Wizard (Divination). Then, on level 12 you have the choice for another feat. The primary goal is to maximize the survivability (i.e. not dying) for the wizard. What feat will best achieve that?
The campaign is a typical D&D campaign in a Forgotten Realms setting, with a mix of dungeon exploration, overland and city adventures, mostly dungeon delving. Party of four, with a fighter, rogue and cleric. The wizard's role is to stand in the back if possible for battlefield control and remote damage, not to engage in melee, but they obviously cannot always avoid that. Sometimes intelligent opponents will decide that they should take out the squishy mage at the back and focus fire on him. The wizard is not the one scouting ahead or checking for traps, that is either their familiar or the rogue, who has high perception due to expertise and high Wisdom. The cleric can cast Aid to bolster the entire team with 15+ increased hit point maximum.
Sometimes foes lie in ambush and assault the group from the side with surprise. I'd like the wizard to avoid dying (going down is fine, as long as they do not die in the end). Situations that took the wizard down, or nearly so, during the first 12 levels include being fireballed, being fireballed multiple times in one round, being attacked with surprise by a Clay Golem, Ropers, a Behir, multiple Shambling Mounds (all different times), and being attacked by a Hellfire Engine.
Playstyle: The wizard will not flee combat and abandon their comrades, unless that is the only way to avoid ensured TPK. We tend to do careful exploration, with a good amount of scouting and divination spells before going somewhere, but even doing that we've not been able to know everything — many dangers are hidden or camouflaged. The vibe is pretty "oldschool", i.e. a DM that sees his role as challenging us with deadly encounters.
Assume the wizard has no special magic items. Their spell list includes all the staples of: mage armor, shield, find familiar, misty step, dimension door, and for remote damage and battlefield control fire bolt, web, fireball, polymorph, wall of force. They do have access to arcane eye and scrying to help scouting. They have contingency, typically set to dispel mind control effects. Pretty much any spell under 5th level is available. They have 8 Str, 13 Con, 14 Dex, 12 Wis, 14 Cha.
Feats I think could be good candidates could be Alert (to avoid deadly surprise rounds, side benefit of higher initiative in combat), Resilient (to get extra hp, side benefit of better ability to keep concentration), and Lucky. Maybe Tough. Among those, which is the best, and what are the reasons for it?
I realize that all feats are good for something, but if you had to pick one to maximize the chances of the wizard surviving, which one would it be, and why that one? While this will differ from situation to situation, when one has to make this choice, one does not have perfect information about the spells, monsters, traps etc. one will be facing. Did you play higher-level campaigns? Maybe what is deadly up there is different to what was deadly in tier 1-2. What was really effective in your experience?
For example, Tough is giving the wizard more hp, but Resilient also helps them to survive Con saves better (and I think due to the collateral Concentration benefit is generally picked far more often than Tough). Are Con Saves (e.g. vs poison creatures) relevant enough for that to matter? Surprise rounds seems to be what often creates deadly situations for the party, and especially for wizards as it means they will be ill positioned. Would you pick Alert over Tough or Resilient, or is it better to just have the extra hp? Lucky can help you make saving throws, on any ability and help with initiative or perception checks against surprise, would you expect that to be more effective than extra hp?
To keep this focused, I'm asking only about Alert, Tough, Resilient, Lucky, and Inspiring Leader. Other feats ar OK to mention, but you should be able to explain why they achieve the objective better than any of them.
Best Answer
Lucky or Tough
Lucky extends your ability to mess with die rolls. It can potentially halve the damage of 3 area attacks per day or with some luck, negate up to 3 enemy attacks. If your DM likes using monsters with very high attack scores (a common practice, albeit one I find distasteful) such that most attacks hit even high AC PCs (a wizard with decent dex, mage armour, and Shield, for example), Lucky will be heavily outcompeted by Tough. Tough will also help in situations where damage is unavoidable. But otherwise, Lucky on average will negate more hp damage than tough will provide hp.
HP is by and large the measure of enemy effects in DnD 5e. Few attacks provide status conditions and those status conditions are often save-ends, or conditions you don't hugely care about as a Wizard (assuming you're using mostly save spells and area effects, anyway).
Exception: Alert
If you are willing to use the first turn of combat to become invisible or teleport (dimension door or likewise) to a position of more relative safety (out of reach of Ropers, for example), Alert is likely to save you from more hp loss than either Lucky or Tough. Observant would theoretically help in this regard as well, but implementation of perception to spot ambushes and the like is generally more patchy - many DMs will just have ambushes 'happen', or rule that situations with invisible enemies or enemies submerged in bogs or whatnot do not allow perception to spot signs of their presence.
Many 'oldschool' DMs will however intentionally negate commonly-used player tactics. Using invisibility in every fight at many of those tables will lead to every single enemy coming standard with see invisibility or some similar means of negating it (regardless of if this makes any sense).
As you can see already, which feat is more useful depends heavily on how the DM views the fights and the game and to what degree they are influenced by player choices (metagaming, in other words). Optimization relies heavily on this information - many of the stronger optimization choices are so because they don't seem powerful to the casual eye. Lucky may make it seem like you're needing to use up resources to stop from getting hit, in a way that is sharply limited per day. Tough lets you take more hits - the DM sees the monsters doing damage to you. Both of these are likely to avoid any particular counterplay on the DM's or the enemies' part in the way that a wizard turning invisible or teleporting away might.
All of that said, the solution likely lies in another castle
Of all these options, probably Inspiring Leader is the strongest one in general (if we disregard the 'to stop wizard getting knocked down' caveat). 48 extra total hp is not to be sneezed at, but it's not for that reason. Inspiring Leader gives you a nice out of game reason to talk to all your party members in-character in a way that can easily be finagled into injecting some strategy or tactics into the characters' actions. You need to go talk to people for ten minutes to give them a significant buff. That's a great excuse to take up some table time suggesting maybe scout a bit, or a party order, or a trap-checking regimen involving a long stick.
Oldschool dungeoncrashing tactics are likely to be rewarded by most oldschool DMs and require zero feats to be used. However, to avoid being seen as overcautious play or holding up the game, an excuse for your character to be the one putting this into motion (especially as a 'non charismatic' character or whatever - personally I hate that 'only the bard can speak to anyone' attitude, but it's endemic) can be very useful, and expending an ASI to 'be a leader' is a great excuse to... be a leader.
That option will likely save your wizard from hp loss more than any other (by ensuring he's ambushed less, mostly, and better battle tactics meaning he's more rarely in harm's way), but is by far the least related to which feat you choose.