Q: Automated drip email (long-term)...how?

Can anyone advise? I have 50+ email newsletters ready (content, copy etc in place). I want to drip these email newsletters weekly to each person that signs up on a newsletter subscriber list... What would be the best way of doing this? I could guess Mailchimp or similar but is there a limit to how many 'drips' you can add to an email drip sequence?? Thanks in advance for any advice. :)