Does Deflect Missiles need to be readied, or can you Attack and then if someone hits you with a missile you can choose to deflect it?
The Attack action happens on your turn, Reaction doesn't have that limitation and is a separate thing that can happen at any time between the start of one of your turns to the start of your next, once.
So yes you can take your Action and Movement and use Deflect Missile should something trigger your reaction to allow it, which could be on your turn as well (although this would be an edge case). You are not required to take the Ready action to do this.
Keep in mind that Reactions are only granted by certain abilities, spells, or (for everyone) the Opportunity Attack.
Deflect missiles uses a Reaction to reduce the damage and if you choose to send the missile back it uses the same reaction.
An attack action on your turn is still allowed, but you would not be able to make any opportunity attacks or deflect any more missiles until the start of your next turn as those require a reaction.