Yes

Ready action requires (emphasis mine):

First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.

The general rule is 1 Action per turn, but then specific rules can override that (e.g. Action Surge, Haste, etc.). I believe that Ready is another specific rule that overrides this as well because while you are using your Action to Ready, what you are really doing is using your Reaction to move your Action to another time.

Attack vs. attack (or does action have a meaning here?)

Upper case and lower case a have a meaning in the PHB, with the former being the Action described under Actions in Combat in the PHB.

When Ready asks you to choose your action, you use the actions listed there. The cases described in the PHB are "Use an Object" and "Movement" for the Ready (since you can only do one.)

In the case of this question, the Action that is being taken is Attack.

Attack Action on your turn

If you take the Attack action on your turn, then it comes with all the fun stuff that happen on your turn. This includes Extra Attack (which typically doesn't happen on a Ready whose trigger occurs NOT on your turn.)

In contrast, you can look at another reaction: Opportunity Attack. In this instance, the language does not say to take an action but to simply make a melee weapon attack. The difference is in the use of Action in the phrasing for Ready.

Actions vs attacks

The language in Ready is to choose the action. Actions are a defined term in the rules under Combat->Actions in Combat.

At other times, there is other language used when specifying melee/ranged/melee weapon/ranged weapon attacks. The language in Ready does not say to Ready an attack (lowercase a), it says to ready an action.

There are also several referenced examples of Ready Action and Extra Attack/Multiattack that reference the On your turn as the important qualifier. Had they not intended a Ready attack to be the Attack Action, then the discussion would have ended there and not referenced the turn requirements.

There are also other specific examples of more than one action on a turn that override that general rule: Cunning Action, Haste, Action Surge, etc.

Intent Support from Jeremy Crawford

The action choice intent (emphasis mine) is also provided by Crawford:

The Ready action lets you ready any action you can take, including Attack, but Extra Attack is on your turn.

Not only has he clearly stated that you take an Action, and that Action can be Attack (uppercase A), but that Extra Attack only functions on your turn.

You must choose an action or movement, but you can omit other information.

Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.

As we can see from this sentence, the minimum requirement is to choose an action or movement. I believe "the action" in this context is anything from Actions in Combat which includes:

one of the actions presented here, an action you gained from your class or a special feature, or an action that you improvise. Many monsters have action options of their own in their stat blocks.
When you describe an action not detailed elsewhere in the rules, the GM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.

So for instance "If X happens, I attack" and "If X happens, I use channel divinity" meet this requirement, whereas "If X happens, I do something" is not specific enough.

The PHB also gives us some examples from which we can make additional inferences:

1. If the cultist steps on the trapdoor, I'll pull the lever that opens it
2. If the goblin steps next to me, I move away

The first example is very specific.

In fact, there isn't any relevant information that we could add to "I'll pull the lever that opens it" to make the Ready action more specific: we can pull that one lever that opens the trapdoor mentioned in the trigger, and even if other levers were present we wouldn't be allowed to pull them.

The first example also shows us that we can choose an action implicitly, because in this example we chose the Use an Object action without naming it explicitly.

The second example is very vague.

There is plenty of relevant information that is missing from "I move away", such as whether we will walk, swim, or fly, and which path we will take. Therefore, the second example confirms that we can be vague and omit relevant information.

However, even this example is not completely devoid of relevant information, as "away" implies a general direction. This suggests that it's best to include at least some relevant information.

Moreover, eventually we must choose whether to walk, swim, or fly, and which path to take. So if our Ready action is vague we can make decisions during the reaction.

Your example.

You can ready an action for "When the Goblin moves, I Attack" as this meets the minimum requirement for the Ready action.
Because that Ready action omits relevant information, you must make decisions during your reaction, such as who to target with your attack(s) and which weapon to attack with.

In particular, you could choose to attack a Goblin, a Bugbear, or anyone else for that matter. However, you cannot unsheathe a weapon during your reaction because you can only use your free object interaction "during either your move or your action", which means that your choice is limited to the weapon(s) that you are wielding when the Goblin moves.