I am a grad student in the US. As an undergrad I managed to save about $20,000, I have no debt, and I have a 401(k) with about $12,000 to which I am no longer making contributions. I am breaking even between income and living expenses and will continue at this pace for at least 3 more years, so while I hate to see this money sit in my savings account I also need to be sure it is safe and readily available in case of an emergency.
According to the answers to the closely related questions here and here a Roth IRA is a safe bet. I am considering rolling my 401(k) into a Roth IRA already since the taxes I will owe right now should be low. If I do this, I can't imagine I would be allowed to contribute my savings as well and also be able to withdraw it if necessary.
Can I rollover my 401(k) and contribute the maximum yearly amount out of my savings, or will I need a second Roth IRA to be able to withdraw whatever I invest? Or should I just invest in a mutual fund or put it in a money-market account?