What is the best self hosting email marketing software/script/cms ?

Mautic if you need a full CRM-like UI and don't mind PHP, Listmonk if you want lightweight Go-based with a clean API and you'll do scheduling yourself. Both handle the campaign + open/click tracking requirements out of the box. The real deliverability problem isn't the software though — it's that shared hosting SMTP is the wrong tier for anything past ~50 emails/day. You need either a transactional SMTP relay (Amazon SES, SendGrid free tier, Mailgun) or a small VPS with PMTA / Postal and properly warmed dedicated IPs. Software is 20% of the problem, sender reputation infrastructure is 80%.