There is also the option to turn the difficulty down, there aren't any penalties for doing so and it's worth it to experience the world/story if all else fails. The skills you pick mainly determine how easy a start you have. Constant Effect Restore Health is extremely useful defensively, with two main benefits: Four points of Restore Health is a good number to aim for, since it is small enough to fit on a Telvanni Cephalopod Helm or Exquisite Jewelry. There also aren't any limits on leveling skills, so even if you don't pick security as a major or minor skill, you could still max it out with enough effort (though it will take a lot of work). The Elder Scrolls III: Morrowind Best enchantment items. You can make up for almost any kind of skill shortcoming with scrolls and potions, so don't ignore them. You can also find items that have the open lock spell effect. If you don't have a high enough security skill, you can cast an open lock spell (and the spell will tell you what level or level range it can unlock), and if you can't do that you can just buy an open lock scroll.
In your example, all locked chests tell you what level they are locked at. I wouldn't say most quests are like that and the ones that do require specific skills usually have workarounds of some sort.