twirap:
I am trying to make a robot that walks on walls.
I guess you're planning to have some sort of walking motion where the cups grip alternately. In that case there will be times where you need both cups to have vacuum. I expect this will not seal imperfectly and will require your pump to run continuously to maintain suction, so in that case you would need to have a separate valve for each suction cup so that you can turn them on and off independently.
I suppose you have already figure out by now that the bigger the cups the better they're likely to work due to the area/circumference relationship, but I suspect your first challenge is going to be to set a weight budget and determine what cups and pump you need to support that weight and then find a suitable power source that fits within your weight budget.