Congratulations on deciding to save money and choosing to invest it.
One thing to know about mutual funds including index funds
is that they typically require a
minimum investment of a few thousand dollars, $3000 being a typical
amount, unless the investment is in an IRA in which case $1000 might be
a minimum. In some cases, automated monthly investments of $50 or $100
might need to be set up if you are beginning with a small balance.
There is nothing wrong with your approach. You now should go and
look at the various requirements for specific index funds. The
Fidelity and Vanguard families are good choices and both offer
very low-cost index funds to choose from, but different funds
can have different requirements regarding minimum investments
etc. You also have a choice of which index you want to follow,
the S&P 500 Index, MidCap Indexes, Small-Cap Indexes, Total
Stock Market Indexes etc., but your choice might be limited
until you have more money to invest because of minimum
investment rules etc.
Most important, after you have made your choice,
I urge you to not look every day, or even every
month, to see how your investment is doing.
You will save yourself a lot of anxiety and will
save yourself from making wrong decisions. Far
too many investors ignore the maxim "Buy Low, Sell High"
and pull money out of what should be long-term
investments at the first flicker of a downturn
and end up buying high and selling low.
Finally, the time is approaching when most stock
funds will be declaring dividends and capital
gains distributions. If you invest now, you
may end up with a paper profit on which you will
have to pay taxes (in non-tax-advantaged accounts) on
your 2012 tax return (this is called "buying a
dividend"), and so you might want to spend some time
investigating now, but actually make the investment in
late December after your chosen fund has made
its distributions (the date for this will be
on the fund's web site) or in early 2013.