Integrating breathwork into my life has been really successful and huge for me so I wanted to give you this as an option. It is not for everyone and if you have any medical issue than I would talk to your doctor before doing this.
There are tons of different forms of breathwork (pranayama). The type that I have integrated into my daily meditation practice is called breath of fire. I do three minutes of breath of fire and then go into about ten-twelve minutes of meditation.
Since I am not a breathwork teacher (but know many incredible teachers who I can refer you to if you are interested) below is a youtube video on how to do breath of fire correctly. It's kind of silly and ends abruptly but it was the best I could find to teach the correct way to do it.
While I think it's important to maintain good posture while doing breathwork, if you are going to go into meditation directly after don't worry so much about sitting up so straight. I think it's most important that you are comfortable when meditating.
It should be noted that it is not good to do breath of fire while you are on your period.
For more information about the benefits of breath of fire check out this article: http://www.gaia.com/article/5-reasons-practice-breath-fire