From the Moldvay Basic Set.
On page B24 it gives five things in order to resolve
There is a special note on movement that if you start in melee special rules applies (explained later in defensive moves) and you forfeit casting spells if you move.
The sequence doesn't say anything about arming oneself. In the section about using oil or holy water they also do not make mention of readying an item. It seems the assumption that within 10 seconds it just happens.
On page B47 it notes that using a magic item, except for weapons, armor, and protective devices, require concentration. While it could be written clearer it probably means that using a magic item is the same as casting a spell. Using it is the only thing you can do in that round. This seems to apply to scrolls and potions as well.
With the exception of magic items and spells, you could generally abstract the above sequence into allowing the character to move and do one significant and time consuming action. Or to abstract it further the character can do two actions but only one of those actions can be an attack or a movement. And casting spells and using magic items consume two actions.
While it could be written clearer, on page B24; Defensive Movement it seems clear that once a character is melee range, they are in melee and that their only option is to attack. Unless they want to do one of the defensive movements to get out of melee, then in the next rounds they can cast spells or fire missile weapons. Provided that they continue to remain out of melee.