To store such a firehose stream of data, you will need approximately 0.3gb of storage per one second of data.
This is if you only collect username, timestamp and tweet, excluding any additional metadata such as data center, likes and retweets, not to mention images and videos.
Full calculation here: https://docs.google.com/spreadsheets/d/1BIAguT9Qvy0GK-dalpQf...