Hi, welcome to the site
If you want a faster car there isnt really a "cheap" way of doing it lol!
New K&N panel filter would increase your gains a little, what i found is that with the K&N filter on it increased the low end speed but sacrificed the top end speed, cant get my car past 100 now. not that we should ever do speeds like this
New cams combined with the Greddy e-manage piggyback ecu also apparently give you alot more power gain and control of your car.
Other things that would really give the wee car a good bit more bhp is a new Manifold, De-cat and rear box.
Also losing some weight out the car e.g. the rear seats, rear panels. But since you said its a family car thats probably irrelevant
There isnt alot you can do for handling, since i lowered my car by 35mm and put 15" wheels on combined with the front strut brace i can take corners alot faster and the car feels more stable.
Last but not least, what most people on here who have the 1.0L k11 have done is to transplant the cg13de engine from a 1.3 micra. A stright swap so im told