Alpha - The higher the better. A positive alpha means this fund outperformed the benchmark by that percentage (1 = 1 percent better). A negative number is bad.
Beta - measures volatility. The lower the better. A beta of 1 means this fund is as volatile as the market. Utilities and bonds have a low beta, tech stocks have a high beta.
Sharpe Ratio - higher the better, measuring risk adjusted performance. Wikipedia has a good example so I'll just plagiarize here:
"As a guide post, one could substitute in the longer term return of the S&P500 as 10%. Assume the risk-free return is 3.5%. And the average standard deviation of the S&P500 is about 16%. Doing the math, we get that the average, long-term Sharpe ratio of the US market is about 0.4 ((10%-3.5%)/16%). But we should note that if one were to calculate the ratio over, for example, three-year rolling periods, then the Sharpe ratio could vary dramatically."
So you should look for funds with at least a Sharpe Ratio of 0.4, if not more.
The ideal fund would have a high alpha, low beta, and a high sharpe ratio. In English that means you want a fund that outperforms its benchmark, has low volatility, and has a higher risk adjusted return than the S&P 500 (10%) as compared to 30 year Treasuries (3.5%).