Upcoming Grand Arena player - asking for advice

Zetas are best sought through ship currency; through GAC rewards; through territory war payouts; through the Executrix ship challenge (you will get there); through the challenge tier 1 level in Assault Battles and through the heroic events. Just do as much of these as you can - and find a guild that can qualify for zeta rewards in Territory war.

If you participate you will quite quickly get to a point where the zeta mats are landing regularly