I always brought propelling pencils for mine. Usually the cheap plastic ones with the rubber on the end. Saved them constantly sharpening them.
Mine started off with ink pens but switched to black biros. I always buy the ones which don't unscrew because one DS can't stop himself dismantleing them and he just ends up with bits of pen in the bottom of his bag.
They may need a proper set of pencils for art. I got those when needed.
A few couloured pencils and fine liners are useful. Mine only took them for certain lessons.
They will need a protractor and compass. It's worth buying a better quality compass and taking it when necessary because the ones in the tins are usless. I wouldn't bother with the rest of the geometry set.
Mine took a shatter proof ruler. The flexi ones look like a good idea but they are not great and the DS that unscrews pens also plays around with flexi rulers.
Rubbers. Mine also took those 'mouse' eraser things that they are not allowed to use
but they didn't take tipex.
Mine also kept a pen, propelling pencil and 6 inch ruler in their blazer pocket. Most of the time that would get them through the day if they got separated from their bag for any reason.
Mine all bought the calculators supplied by school to start with. It is easier to start with if all the class have the same make.
When they first started secondary they always took everything in a pencil case but later they carried stuff in their blazer pocket or in various pockets in their school bags.