You're in luck! Mazdaspeed3 dampers are crap from the factory! So pretty much anything you replace them with will be a huge improvement.
Personally, I'm running Koni FSD's on the stock MS3 springs. It hasn't been long but the car just seems to do everything better. Is it the best? Depends what you're trying to accomplish. All I know is that I can safely tackle back roads at much higher speeds than before, with better ride comfort, ride quality, and stability, especially under braking on bumpy surfaces.
But there are other options for maximum handling. First and foremost perhaps, the very adjustable coilover kit from Mazdapseed. Double the spring rate, adjustable ride height, and adjustable damping. Most people who have them seem to like them a lot. I've seen them priced as low as $1000, without the camber links you need if you're going to go much past the minimum drop.
If I were going for maximum lap times without coilovers, I would seriously consider the AWR valved Bilsteins Voigtlander race springs (not currently shown on their web site but they have them). It's a very racy combo, from what I've heard, very fast, but not particularly comfortable for every day use.
There's also the Koni Yellow and Eibach Pro Kit combo that's specific to the MS3, that most people like, and some people don't.
In my experience though, just installing FSD's fixed what Mazdaspeed screwed up. Like I said, it just does everything better. It also taxes the tires though, the next weakest link in the chain. With the OEM setup I ran out control and stability, but with that mostly solved, I'm running out of tire grip.
Nice problem to have from just a damper change, IMO. Especially on the crumbling roadwork in my city, state, and county, with no budget left to improve them. All I really know is that I have a comfortable yet fast setup for the conditions I encounter every day.
