I put almost all of my savings into total stock market index funds. I use Vanguard so the expense ratio is 0.05%. Dividends are automatically reinvested so I don't have to worry about that -- from my perspective dividends look no different than the fund's value going up.
Here are some resources that explain why to do this and how:
https://www.reddit.com/r/personalfinance/wiki/investing
http://www.mrmoneymustache.com/2011/05/18/how-to-make-money-...
There are endless ways to diversify. For example, my portfolio is "diversified" across all stocks. But the entire stock market goes up and down, so some people diversify by putting a percentage of their savings in something else, like bonds or money market funds. These tend to have lower historical average returns than the stock market, but they won't necessarily go up and down at the same time so your savings will not fluctuate as much.
I haven't looked into paying less taxes, aside from maxing my 401k.