i believe i know the analog devices chips your using, if you just want a plain hard square wave out with no amplitude control, all you need is to feed in your set point to the other input of the op amp / comparator and as it crosses the threshold will slam from one rail to the other,
comparators are better suited than op amps for this as they are made to slam rail to rail, where op amps are more made for a wide control range sometimes saturating at the rails,
as for what to use, as you are wanting to pull and push a decent whack of current i would recommend a fast but lower current op amp followed by a simple push - pull amplifier (pnp and npn) yes you may loose 1 odd volt off each rail but it makes dissipating the heat easier, and you can equally use the base resistances as a rather nice form of current limiting,
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now that i furthur read it, you want to control the offset.. well now if it was just a simple comparator it would be slamming rail to rail when one input becomes higher than the other which leaves little to offset,
however if you both want to control the amplitude of the output, as-well as its offset, (e.g. 3V p-p square wave centered at -2V) it is still possible, but requires an op amp,
for this you begin by summing in a offset voltage, in your case likely input of 3V fed in through 10K, and your offset voltage of -1.5V (for zero centered waveform) summed in through another 10K, this can either be off another pot or buffered through another op amp, and i would recommend buffering it if you wanted a linear response in offset, with a range depending on how far above zero you want it,
next up would be the gain, this can be as simple as a potentiometer between the output and the inverting input with another resistor between the inverting input and ground, you size this likely for a gain of 8 (+-1.5V into +-12V) allowing you to go from full rail to rail or decrease and offset as you please,
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for your final point, use a push pull comparator, only some are open collector type that need a pull up resistor,