All three are ok. The first one is the most common.
The second one emphasisemphasises "Heute". It would be a common way to answer the question "Was machst Du heute?"
The third one is the most uncommon. It emphasisemphasises "Einen Brief". Maybe you would use it to answer the quesion "Was schreibst Du heute?" - but the most common answer would be simply "Einen Brief."
Edit: As Felix Dombek pointed out in the comments, the third example could also emphaseemphasise the word "Einen". So it could be the answer to "Wie viele Briefe schreibst Du heute?" - "Einen Brief schreibe ich heute."