While not a resident or attending yet, I am a 4th year medical student looking to go into orthopedics, and have spent time over the past 4 years learning about personal finance and investing, specifically geared towards physicians, to best prepare myself for the coming years.
I'm assuming you're a current medical student and taking out federal student loans. Depending on your year, with the restructuring of how interest has been calculated, your combined interest should be 6-7%, which is quite high. There are private companies which are as of 2015, starting to refinance federal student loans for residents down in the 4-6% interest range. This might not seem like a lot, but if you're sitting on 2-300,000$ of student loan debt, that refinance can ultimately save you 10's of thousands of dollars. If you go this route however, you are not eligible for IBR, PAYE, REPAYE, or any of the other graduated payment systems offered by the federal government, and you're also no longer eligible for loan forgiveness after 10 years (probably wouldn't qualify for this anyways, unless you go into peds ortho, and know you want to work at a larger children's hospital -- you need to be working for a non-profit hospital to qualify for loan forgiveness)
Whatever you choose, I would highly recommend making SOME payments on your loans during residency. First, because it will help knock down some of the interest you've been accruing during medical school, but more important than that is because it will help instill in you good budgeting/spending behavior, which will be important as an attending as well.