You seem to misunderstand what bonus actions and readied actions are.
The action economy at first can be fairly confusing, but once you understand it it makes things move much smoother.
One thing to note is that each type of action can (usually) only happen once per round by each creature - player or not.
This is your run-of-the-mill stuff you do. Usually attacking, casting a spell, et cetera. If you are not sure when something is another type of action, it's usually a 'typical' action. This can only occur on the creature's turn. Note that movement is completely separate from an action.
Bonus actions are just that - an action that you do as a bonus! Sometimes a spell or other such ability will say something along the lines of "As a bonus action...". This means that it does not take your singular action. This also occurs on the creatures turn, but can happen before or after the main action (depending on the ability - make sure you read it in full!) However, you can only take a bonus action if the ability you are using allows for it. You cannot attack with an action and decide that you want to attack as a bonus action, unless you have something specific that says "You can attack as a bonus action as well as your main action".
This one is a bit tricky. In order to ready an action, you MUST sacrifice your main action by stating what you want to do, and when you want to do it. Using your example, the goblin may use its action as "I ready my bow to shoot it at the first person who spots me". This skips its action, and saves it for later. The trigger ('...the first person who spots me') can happen at any point until the creature's next turn, but must be declared as an action. You can also, instead of using a standard action, ready movement up to your move speed in response to the trigger.
Reactions are similar to bonus actions, in that you cannot just decide to take them. Only abilities that state 'As a reaction...' or similar can be used as a reaction. They differ because they normally have a trigger event. Consider the spell Feather Fall, which has the casting time of "1 reaction, which you take when you or a creature within 60 feet of you falls". The trigger to allow you to take it as a reaction is "... you or a creature within 60 feet of you falls". Ergo, this does not have to happen on the creature's turn, but once again they only get one until their next turn.
There are certain things you can do for free. The PHB lists some of them, such as pulling a lever, picking up a small object, et cetera. This doesn't take any sort of real action, it's just something you do.
Based on your description, it almost feels like you're 1. Bouncing the turns around and/or 2. Allowing a creature to have multiple actions of the same name on the same turn. To help with this, have an initiative tracker of some sort, and get every creature's action/bonus/free when its their turn. If the goblin runs away, and the Wizard is up next, don't let the Barbarian just run after him when he feels like it - it's the Wizard's turn! (Unless the wizard skips his turn - which he is allowed to do. He can just sit there and twiddle his thumbs if he desires).