Originally Posted by
chaimdan
I'm looking for a program that has a good reputation for cheap redemption and valuable miles...
I doubt that any of us here have much idea what this is supposed to mean. Your questions are so vague that they are essentially impossible to answer.
I suggest that you spend a bit of time studying the wealth of info offered on this site and then ask some more informed questions.
I'll get you started, however. There are 3 major airline alliances: Star, OneWorld, and SkyTeam. The idea is to accrue miles in any member of a particular alliance and then use the miles on another. For example, I'm a UA guy. UA belongs to the Star Alliance (*A). I could accrue miles on UA flying around the US and to Europe and then use said miles to buy award tickets on Singapore Airlines (SQ) to Asia.
Good luck and good studying!