Welcome to 1200.com. An L series in a 1200 is reasonably common here, so we should be able to help you. There's also a website called Ozdat.com, which has a good amount of information. Where about's in the world are you? Depending on where you are, I can suggest 4 or 5 different places to get stuff like pistons, cams, etc. Hope the kids have a good time racing the car.
As for what to do to the engine, sometimes it's better to just get the car running with a stock motor before building a hot motor. Just a 32/36 dgv weber or a single DCOE weber or D'ellorto , some extractors, , an electronic distributor from a Series 2 Bluebird or a kit in a stock distributor & a good coil should be all you need to get it running. A rebuild to 86mm pistons with some flat top pistons, a bigger cam with better valve springs, twin side draughts & all the other things you can do can probably wait til the kids have learnt to drive the car. I can remember how fast my first 1200 with a 1400cc A14 seemed to go when I first started racing it, but by the end of the year I was driving to the limit of the engine, so a 1600cc A15 was built over the off-season. That first year was great, but if I'd decided I couldn't afford racing, I wouldn't have spent a whole lot of money finding out. I did the same thing a few yers ago when I put an L18 into a Sunny coupe. The engine was stock inside, but we had 2 dcoe's, extractors, electronic dizzy, lightened flywheel. The car handled beautifully, stopped well, but was limited in top speed, if you can call 190 kmh slow, so a swap to a worked L20B was on the cards when the real world got in the way. Still have the car & an L20B with a close ratio R30 5 speed, so I hope to get it running this year.