403(b) is the same as a 401(k), except it's used by different employers. This means - you should definitely be contributing, since the money will be not subject to federal+state taxes, and it's a very good way to save.

However, the old 401(k) should go into an IRA account, for the reason I list in the post: more investment choices, more control, more flexibility, option to convert to Roth IRA. The inconvenience is minimal. You'll open the IRA account, move the funds, invest them, and you can forget about them.

When you say "money market account", do you mean a money market fund, otherwise known as "cash", also known as "0% yield"? Don't do that. The account should be fully invested in investments - something other than cash. To give more guidelines, I'd need to know more about you - at a minimum, how far you are from retirement, and how strong of a stomach you have, i.e. how much volatility you can tolerate.

If you are about 30 years away from retirement, and you have the fortitude to invest and then never look at your IRA account again (and not sell out of equities after they drop 40%), then you should have at least 80% in equities, about 40-50% US and 30-40% International/Emerging Markets. I'm partial towards emerging markets, and towards the mid cap space in US.

What I learned about myself is my risk tolerance is much less than I thought. I look at my investments every day, and when they drop in value, it bothers me. So I'm going to have about 20% in fixed income in my investment portfolio overall, with most of it in IRA and Roth IRA.