So I'm making a new Spellsword which is gonna be more or less one handed and spell with robes intially and later on enchanted armor. Being completely new to this aspect I'm wondering if it's a viable long term strategy to forego one magic skill tree and instead wear an enchanted chest piece with cost reduction and regeneration?

I'm going to focus on One handed, Destruction, Alteration and Restoration, backed by Enchanting, Smithing and Light or Heavy Armor and my initial thought is to only grab damage increasing destruction perks and nothing else while maxing out most of the other two magic trees. Is the illusion tree good for anything else than crowd control?

I would like some input from those of you experienced with playing Spellswords the Skyrim way, as I intend for this to be my main character which I will use to finish the main quest.

Spellsword more than anyone benefits from Restoration with Respite perk. You can get by with no stamina increases, leaving all level ups for health and magicka.
You already have seven skills without illusion, don't want to spread the perks too thin. Illusion can be fun, but tops out as far as enemies affected are concerned, unless you invest in the perks.