No, you do not need to ready the reaction spell.
How do you prepare a spell?
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell’s magic requires concentration.
Do you have to roll to hit spells?
The rules don’t say that any check is required to make a spell work, which is how we know that spells happen automatically: casting requires no rolls to be successful in general.
Do you have to roll to cast a cantrip?
Yes, cantrips work just like normal spells, and thus you still have to roll Cast a Spell when you want to cast them. The only difference is that you get to prepare cantrips for free every time you Prepare Spells.
Do you have to hold a spell to use the ready action?
No, because the Ready Action requires you to cast the spell as normal and then hold it, releasing it with your reaction later. You are using your action to cast the spell on your turn. PHB pg. 193 under Ready, emphasis mine:
Can you use a reaction spell during your turn?
You can still cast a reaction spell during the same round during another person’s turn, just not your own. A spell cast with a bonus action is especially swift. You must use a bonus action on Your Turn to cast the spell, provided that you haven’t already taken a bonus action this turn.
Can a bonus action spell be used during your turn?
No rules prevent casting a Reaction spell and an Action spell. If you cast a Bonus Action spell, you can’t cast a Reaction spell during your turn (uncommon but possible), but you’re free to cast one once your turn is over. Trying to think of a situation of using your reaction on your own turn.
Can you cast more than one spell in a turn?
Rules dont forbid casting more than one spell. There’s only one restriction, on p202. If you cast a spell as a bonus action, you can only cast another spell on your turn if it is a cantrip and has a casting time of 1 action.
