I suggest the LM324 and LM358 from personal experience. These op-amps are able to work well under low voltage supply situations and can operate sufficiently well with supply voltages of roughly 3.2V and above to about 18V. these chips work well for applications such as amplifiers, schmitt triggers with hysteresis(LM324 is best for this app) and other applications that require the use of comparators, etc.
Datasheets tend to help a lot if you are willing to take a few minutes to read through them, you tend to find a lot of helpful info there that beats posting on these sites and waiting for replies.
All the best