Here the choice is quasi infinite.
Some pumps are operated manually, some function with electricity, and some even come with compressed air tanks! For the purpose of this series, hand operated pumps will be more than sufficient.
You might wonder: what about inflating twisting balloons with the mouth?
Well, I usually do not recommended it. Although if done correctly, it should not cause any problem; if done the wrong way, it has the potential to harm your lungs, your eyes or your ears. That is if you do not faint first. In any case, it is not very hygienical, just think of the myriad of rather intimate lung germs that will be spread to the children each time a ballon pops.
Back to the hand pumps.
To inflate 260 balloons, I essentially use either one of those two.
The smaller one comes in handy and can be carried anywhere since it doesn't take much place. Its main drawback is that it requires your elbow to do a few goings and comings before a balloon is fully inflated. That means extra time, and occasional muscle or articulation aches and pains.
The bigger one, that stands on its own on the ground, is way more bulky. However, it inflates a 260 balloon with only one movement of the hand, which results in less time and less effort. One further advantage is, that the balloon inflated with it, offers a smother and regular surface from top to bottom.
You can find both types of pumps easily on Internet, allbeit with a diversity of quality and price.