Hostinger Domain Transfer Assistance Needed

I bought my domain through Hostinger, but they have suspended it more than once without a clear explanation. To avoid another surprise, I want to move the domain to a more reliable registrar right away.

What I already have
• Full access to the Hostinger control panel and the registrant email address, so I can receive and approve any confirmation links.
• My nameserver records and DNS zone settings backed up.

What I still need
• Guidance on unlocking the domain inside Hostinger and retrieving the EPP/Auth-code.
• Step-by-step help initiating and completing the transfer at the new registrar. I’m still deciding between Cloudflare Registrar, Namecheap, or GoDaddy, and I’m open to your recommendation if you have a strong preference.
• Smooth propagation of existing DNS records so the website and email stay live throughout the move.
• Confirmation that the transfer has fully settled with the new registrar and the domain status is “Active”.

Acceptance criteria
1. Domain shows as successfully transferred in the new registrar’s dashboard.
2. WHOIS lookup reflects the new registrar and “clientTransferProhibited” status.
3. Website and email experience zero or minimal downtime (minutes, not hours).

If you have handled Hostinger transfers before and can manage the whole process quickly, please outline your plan and the expected timeline when you bid.