For budget Sigil focus I’d play Vitality Cabalist. The key item is Vampiric Bonewall
There are a lot of accessible items for Sigils so itemization could look as follows: Sigil Items
You can later farm Dark One’s setup which converts part of Sigil’s Chaos damage.
Later you get Radaggan and switch to Acid (natural choice because the set converts a lot of Sigil damage to Acid) or stubbornly stay with Vitality [1.1.9.1] Cabalist 12-13 Sigils. 100 SR. 150-170 5m 20s. Crate of Entertainment. Ravager. Avatar and other bosses
Or Sentinel:
- (Vitality Beginner) [1.1.9.1][HC] Beginner's Shield Caster Sentinel - SSF + Viable for first character
- (Acid Radaggan) [1.1.7.1] Sigils of Radaggan - Acid Sentinel - crucible 170 clear - YouTube
If not planning Radaggan perhaps you could stay with Dark One’s and then Conjurer is an option as ya1 said to have this silly healing from Wendigo Totems. But for me Sigil focus means getting -recharge for it which Radaggan (and Trozan) provides.
If playing Conjurer you could theoretically switch from Dark One’s to Trozan once you farm it but I don’t know if Trozan Conjurer is appropriate for Hardcore.