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I'm playing a 5e campaign as a Fighter, planning on becoming an Eldritch Knight.

Thus far (we're still level 1), the DM has been resolving attack rolls against us by telling us the result of the attack roll, and asking us if it hits:

• 
  DM: "The goblin takes a swing at you!" (rolls behind DM screen) "Does a 19 hit you?"


• 
  Player: (looks at character sheet) "Yep. Ouch!"

This has worked fine so far, since there isn't really anything any of our characters can do about being attacked, and you can't derive very much useful information from knowing what a monster's modified attack roll was. However, in a couple levels, I'm going to learn to cast spells, specifically the Shield
spell, which changes things a bit.

I know that I don't have to declare whether or not I cast Shield until I know whether the attack would hit me, but am I supposed to know the exact modified attack roll result when I decide? Or should the sequence of events be more like:

• 
  DM: "The goblin takes a swing at you!" (rolls behind DM screen) "What's your AC?"


• 
  Player: (looks at character sheet) "It's 16."


• 
  DM: "Okay, the attack hits."


• 
  Player: "I cast Shield in an attempt to protect myself, raising my AC to 21. Does it still hit me?"


• 
  DM: "Nope, it glances off your magical barrier."

This is important because if I know the attack roll result, I know whether it's worth bothering to cast Shield, whereas if it's hidden from me, I have to guess whether the attack beat my AC by 5 or more.

Whether it hits

Usually, the DM asks your AC before the play, and they take a note behind the screen. When they roll an attack behind the screen, they can immediately determine whether it hits or not. In this style, the DM only announces the hit, and not the total roll.

However,

your group has been using the other style: announcing the total attack roll.

It works with your group. Don't fix if it does not break.

You don't have to worry too much about "metagaming" the attack roll. What your player knows should be instinctively known to your character. If I'm the DM, if the roll can't be beat by Shield, I'll narrate the attack as a very fast attack, and you can't react fast enough to cast Shield.

According to this tweet by Mike Mearls, you're supposed to know with certainty whether the shield is enough to protect you or not, so that you can't waste the spell.

This is also how I have seen it be done in every game I have played. The DM announces the attack score, and the player compares it to their AC and announces if it hits or not.

Shield

Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.

As the spell states including the triggering attack, meaning when you confirm the attack as a hit, you then can choose to cast Shield as a reaction. RAW

You should know if the attack hits or not, any statistic ventures into the realm of metagaming. Now, a certain level of metagaming will happen, but is not a big issue if you leave that for OoC (Out of Character) times.

Take a moment to actually put yourself in the situation, a round is 6 seconds, as soon as you feel that weapon strike (that nanosecond the weapon would make physical contact, not just guessing it would) against your body, you mutter some words and wave your hand. Then POOF, you acted just in the nick of time to bring forth a barrier in hopes to block said strike.

If you know if the attack roll was too high enough to use the spell, then the spell is pointless. You are taking a chance to prevent yourself from injury or worse.