Welcome to the forum Danielson! I can’t help to say that in Mr Miyagi’s voice in my headw. haha.
Check out some build threads there may be som good ideas in there for the upgrade.
The "standard formula” for Brakes and Suspension for an M101 Sirion is basically:
BC Racing Coilovers
Copen Front Calipers and Discs
That will make it handle much better, you can set the ride height you want and will be a good improvement in braking. Coilovers are off the shelf, Copen gear isn’t too hard to find and it will all fit without much hassle.
There are (of course) alternatives to suit everyone’s budget / mechanical knowledge / use of the car:
You can mix and match suspension parts from other vehicles, Both Daihatsu and others. Have a trawl through the forum, but I seem to recall a certain Hyundai Excel model, Hyundai Veloster for the rear shocks. Copen Front struts or modified VW or Siliva parts. These can be teamed with shorter springs to achieve a lower ride height and better* handling.
*If you’re looking into taking the car on the track, you may want to then setup the car in a specific way, with potentially factory front struts and a much stiffer rear for proper weight transfer/handling. It is a rabbit-hole of trial and testing and often at odds with the more ‘street version’ of “I just want to lower it and make it handle better”.
Braking - a less common option is a slightly larger (larger than Copen) caliper and rotor from a Daihatsu Materia (and others maybe). You can look to convert the rear drums to disc brakes with a variety of parts (including MX-5 gear), though requires more customisation. Of course you could stick with the current caliper and just get new Rotors and Pads as a ‘first-step’.
Bracing - there are various internal and external bracing available to stiffen up the chassis. Also there are rear sway bars that may or may not help given the simple torsion beam rear suspension.
Bushings - given the age of these cars, the bushings may be worn. So replacing these will definitely help with the feel of the handling, these can range from easy to replace by hand to needing parts removal and bushings pressed. Siberian Bushings from Russia had great options. Compact Motorsport in NZ is also a great source. Of course through any Japan Auction (Buyee etc) site you can usually find what you want (though more expensive). Daihatsu’s in general are also popular in Malaysia due to one of their brands using Toyota/Daihatsu parts and so there is a lot of re-sellers of parts with NMF being regularly used/praised by Australians.
Wheels and Tyres - given the low amount of power these cars make, lighter parts always helps as does having more rubber on the road. So aftermarket rim/tyre combo’s can help with the handling too.
Enjoy searching around all the Sirion Builds for information & inspiration!