Twitter hashtag background streaming

My recommendation would be to use both, but if i had to pick one i would say a formal twitter account.

As you yourself noted in your question both the hashtag and account serve two very different purposes but work well together.

The hashtag is a great way to attach a subject to a tweet. Although getting people to use your specific hashtag can be a challenge at times.

A formal twitter account would allow let other twitter users engage with you ( or whomever is running the account ) on a more intimate level. While at the same time letting you broadcast and start conversations with other people.

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You need to create a so called Twitter Bot which will tweet everything containing a certain hashtag.

There is a really good tutorial on this here.