I once had a successful missile-less game, success in : I stopped because 1hour IRL for a day in-game and battles that always lasted thousands of turns and 5seconds... My only missile was a big planetary bombardment with its own class of ship to operate.
Trick vs missile fleet is VERY good small sensors/fire control, multi-layer approach, speed and decoy.
All my fleet were based around a very big carrier with all long range and active sensors, tons of armor/shield and PDD.
I had meson fighters (could hunt missiles and kite the swarm things) but fighters are such a PITA to manage I didn't want to make more than few per carriers.
One kind on destroyer, small with only medium sized rapid-fire lasers to avoid getting targeted while ofering fast forward AM support (use picket).
Lots of frigates with medium range lasers that had two possible fire control so to get AM and AS (fast and long range enough to get 2-3shots per volley). They were intended to get ride of fighters of shields on of preservers.
The cruisers with few gauss in close range (task force) AM and in centerline the main battle canon, a very long range slow laser (the only fire control that could not reliably see missiles).
I often had a OAP/TK that would be bigger than the carrier but with no sensor. Again full of armor and PDD since it's mass make it prime long-range target.
You have to be able to engage missile from far, even if it's not very effective. You need to run away when they get in-range to have most shot at them.
The problem is if you don't have enough relyable AM, then you rely completely on your speed to disengage or the enemy to run out of missile and risk loosing everything. More so with sufficient speed, you don't have to invest in turrets.
Don't invest in individual protection (armor, shields, PDD) except your baits.