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I'm looking to run a squad of 10 Cataphractii Terminators in a Storm Eagle when I start my pre-heresy Emperor's Children, but I'm not entirely sure how best to equip them since I'm not very familiar with all the 40k rules.

Does anyone have some insight on this?

Firstly, HIGH FIVE !!!!
i also do Pre heresy EC

ok on to the tactics.
i run 2 squads of 5 both loaded out differently, i find they both work well.
the first squad has - 2 pairs of lightning claws, 1 chainfist, 1 hammer, 1 powersword, 1 heavy flamer, 2 combiflamers. - these guys are really good for killing anything with 3+ or lower armour.
the second squad has - 1 pair of claws, 2 hammers, 1 chainfist, 1 power weapon (havent decided which yet), 1 plasma claster, 3 combi plasmas - they kill everything extremely well.

so i guess if you want to be good at killing anything you could maybe go with this:
4 pairs of claws
4 hammers and combi plas
2 chainfists with plasma blasters
????

that would kill anything reliably, especially coming out of a storm eagle.

hope this helps

honestly i dont really give my cataphracts any cc weapons except a chainfist to deal with vehicles, i find power axes/swords and mauls deal with anything effectively. Putting all your cataphracts in a stormeagle tho, thats a lot of eggs in one basket, but if your are doin that, combi weapons and heavy weapons are the way to go really. If in the storm eagle the plasma heavy weapon is the one to go for i reckon. Course if your far away, the reaper is pure gold.