I want to store a hash (of a tweet) in a way that is :

 - Censorship proof
 - Public
 - Unchangeable
 - Persistent
 - Non centralized
 - Less expensive as possible, obviously free if possible

Technology offered by the blockchain seems to fit my needs.

Since I don't want to run my own blockchain because I didn't find a way to do it for free (or does it makes sense to run my own blockchain on my own server ?).
After reading on the subject, I came up using an existing coin (Bitcoin ?) and as you may guess to the `OP_RETURN` field in a transaction. 
But storing my hash in that field is really appropriate ? 

Can't I use other coins for that, or create my own coin ?

Since I will store lots (3k/day) of tweets, will it not be expensive to do so ?