Essays: Lamy Safari Rollerball(M63 cartridge). Has a very large point size (1mm) but is exceptionally light weight and writes very fast (for me). Expensive for cartridges, you would want 2 to cover you for your entire HSC (2 will get you through English advanced + Ancient history with enough left for one more 2 hour paper). M63 is a very deep black and will do fine with scanning.
Mathematics: Uniball eye micro (0.5mm tip). This is also generally my choice for physics and chemistry. Deep black will be fine for scanning (with the 0.5mm tip and above anyway, unsure for smaller tips)
I have terrible trouble writing and these go best for me. I don't think either of these would be a great choice if you are left handed (rollerballs are very inky and smudge easily) and they do not work with white out (I'm told we cant use white out anyway)
If you prefer a ballpoint the Lamy Safari ballpoint (M16 cartridge, I prefer the medium tip) works alright. It is noticeably heavier than the rollerball safari but writes well. It has a lighter colored black so may not be suitable for scanning.
It is probably a bit late to get the Lamy ones now unless you want it for the final week (but thread could be useful for 2013). If you choose to get a Lamy make sure to get extra cartridges, the M63s don't last long and i've had M16s go prematurely (even through they should last very long). They are also decently expensive (especially for many refills) but honestly the rollerball safari is worth the cost for me.