I run to work and back most days and have been for years.
I wear a Lowe Alpine 'bum-bag' made for hiking. Wide main belt, and two restraining straps to stop the contents wobbling. I can fit in wallet, phone, keys, maybe a notepad or other small items if I have to, even a waterproof shell in winter. If it's just the essentials, I hardly notice it and often do fartleks or tempo on the way home. When it's overfull (e.g. books, papers) I have to yank on the tensioning straps a few times during the run.
Any proper backback always affected my style and got in the way, or gave me backache.
If you have to carry important papers, mail etc then fold them in half or roll them then put them inside a plastic bag, otherwise the contents get steamed gently while you run.
Hope this helps..