Hey,
I recently did a project where I needed to generate a square wave. I won't tell you which is better, but I can tell you what I looked for when choosing my op amps. Some things to consider:
1) Input offset voltage. How much DC offset can your pulse tolerate? High power op amps tend to have higher offsets, at least from my experience. Related to that...
2) Input current bias! Same kind of deal. And related to that...
3) Input impedance! If it's too low, you're really not amplifying what you want.
4) Slew rate, measured in volts/microsecond. It's basically your maximum slope for your waveform. This probably isn't super important because you're not going into frequency ranges where slew rate might have an effect.
5) Gain bandwidth. Again, probably not a concern with kHz applications, but something useful to note.
6) Output impedance. As low as possible! Related to that...
7) Output current. Many opamps don't really have a high output current, so if you plan on driving something, check the output current first! The first op amp I got for my project only could supply ~5mA, but I wanted to drive something that needed about 20mA, so I had to switch my op amp.
8) Number of opamps/package. That's more of a cost and area thing.
9) Supply voltage/current. Do you have access to a double supply, and how large? And how much current can you afford to draw? Is this powered by battery or plugged into a wall? Remember, your supply voltage is also related to your maximum amplitude!
Anyway, there were just a few points I considered for my project. A lot of these may not have an effect on your project, but in general they were points of information that I thought were useful in mine. I hope this helps you pick out the proper op amp!