Gain or amplification
For voltage op amps (the usual kind) you need to do 3 things. First, find the maximum gain you need. Second, multiply this times the greatest frequency you need, and then multiply this by at least 10. This is called the gain-bandwidth product. Finally, multiply peak voltage times the highest frequency times 2 pi. This is the required slew rate. 

Now check that your gain-bandwidth product is less than the op amp gain bandwidth. The reason for the added factor of 10 (or more) is because the op amp needs what's called excess gain in order to provide accurate signal amplification. If the op amp's GBW is OK, check the slew rate requirement against the op amp slew rate. 

Finally, you have not specified the load which the op amp must drive. If this is something benign, like an amplifier you should have no trouble. On the other hand, if you're trying to drive a load such as a speaker, you may need to learn about amplifier loading.