First off, you should go read the wise words of the legendary jlcollinsnh. He's been retired for some 30 years and is - believe it a or not - a better writer than MMM. Start here:
http://jlcollinsnh.com/2011/06/08/how-i-failed-my-daughter-and-a-simple-path-to-wealth/I'm a young adult and this is how I started investing.
1.) I went to vanguard.com and said I want to open an account. The first account I opened was a roth IRA. In a roth IRA, I pay taxes on income I make, put it in, and can withdraw it tax free after 60. There's a $5500 yearly addition limit.
2.) I bought $1000 of shares in a target date 2050 retirement fund (through the online web interface). I picked the date by finding the year I would turn 65 and getting the closest fund. The fund buys 4 funds: US total market index, International total market, US bond market, international bond market. The asset allocations automatically change based on your time horizon until retirement.
3.) Every paycheck, I put at 25% of my money in there (I don't make much yet)
This is my plan for the next job:
4.) Open a 401k through the company that hires me.
5.) Put 25% of every paycheck into a total market index fund
6.) Open a taxable brokerage account at vanguard and put "extra" money in there.
To answer your question about compounding: There isn't really a "compounding rate" because you're actually buying an ownership share of a real company (through a mutual fund). In good years, that company makes more money and in bad years it might lose money. The value of your shares swings as a result. The market isn't like they teach in algebra. It is volatile. The market gyrates up and down. But overall, a total market stock fund grows (compounds) at 10% per year. However, you might see a return of -30%, 2%, 20%, -4%, 12%, etc. In the long run, you can probably expect a 10% return.
At the same time, the value of the dollar is decreasing because of inflation. Inflation eats up about 2-3% per year, so your after-inflation return is about 7%.
To save for your child's college, you should open a 529 plan (it's designed for college savings).