Total newb to investing

Hi Everyone,

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I am one of the millions of Americans whom the public school system failed by not teaching me anything about how to handle money.

My Wife and I recently inherited a substantial amount of money. After buying a house and a car, we have about $100,000 left over that has been sitting in a savings account not earning us anything.

I make good money and have no debts besides my mortgage payment. My monthly salary is enough to cover all of our living expenses. I have two union pension plans, so I am not terribly worried about saving for retirement. I am more concerned about wanting to maximize returns on the $100,000 in cash we have. That being said, I'm pretty cautious and distrustful, so I'd like to be safe with my investments.

I need some help with what to do with the remainder.

Some first steps I've already taken based on things I've read here and elsewhere:

1. I have opened a roth IRA and immediately committed the max $6,000 to it.
2. I have opened a roth IRA for my wife and committed the max $6,000 to that as well.

After that is where I need some guidance. I am planning on transferring about $80,000 from my savings account over to Schwab and putting that mostly into index funds. How should I approach this? Should I diversify into three different index funds?

Thanks in advance for your help!