Actions are much less defined. In our 1st edition game experience, our game play is "fast and light" - combat happens quickly, players cycle through their turns easily and there isn't a lot of tactical thinking going on (yes, we do use minis). This has it's pros and cons.
In a sense, you're already playing 5e. What little we got to hear about the 5e demos paints it as a very DM-driven system. Not a lot of system, with the DM filling things in with his best judgement.
1e AD&D did not have a 'fast and light' combat system, unless you ignored a lot of rules - which almost everyone did. 5e sounds like it's going to default to not having many rules and letting the DM handle adjudicating things. Which'll be fine for experienced DMs, but might discourage newer players from getting behind the screen.
Another side of this is player dependent. In 4e, a player who is unfamiliar with the rules can ask how something works and get a codified answer straight from the rules. Can I move up to the door, draw my sword, open the door, and charge? No, because that's 4 actions. Cut and dried. Ask a 1e DM that and some might say yes and others no. Some players don't feel the need to ask how something works, they just say they do it.
In 1e, that was encouraged. The DM and player were both told that the player tells the DM what he'll do, and the DM tells him how long it'll take, even if it's more than one round. So a player might say, "I jump over the table, up end it to use as cover, take the two flasks of oil out of my pack, make molotovs out of them, take one each in hand, stand up, shout "burn baby burn!" and throw them at the orcs!" That's legit. It might take 3 or 4 rounds, but it's a legitimate action declaration.
How should actions be handled in 5e?
I'm very leery of pushing things to 'optional' status. You rarely see games with lots of optional rules played in anything other than two ways: all options used or 'default.' Default will see a lot of play, if it closes too many doors it'll put off more experienced players. Anything-goes will see a lot of use. If a character that doesn't avail itself of every option isn't viable along side those that do, those games will be for elite 'system masters,' only, and will tend to put off more casual players.
Whatever actions the game uses, they all need to be useable in the default game. They may not all need to be spelled out, but they should all be useable.
For instance, in the basic games actions might be:
Standard: You can attack with a weapon, cast a spell, or CHARGE!
Move: You can stand up or move your speed or stand up if prone.
Minor: You can open a door, draw a weapon, or pick up, stow or retrieve an item.
Other: Your DM will let you know other things your character may be able to do on his turn or between his turns. For instance, when an enemy runs away on his turn, your DM may give you an opportunity to attack him as he flees.
A player who's accustomed to that could play at a table with other players who use OAs and interrupts and not be entirely confused or ineffectual.
In other words, the complete 'action economy' needs to be present in the basic game, it just doesn't need to be detailed or meticulously developed.