I have my own well and I think it could get messy sharing well output with others. Just a few thing to consider:
Why are the sellers moving? How well has the well sharing arrangement worked out for the sellers in the past? Any disputes?
Who pays the electric bill for the pump? Or is it split 3 ways?
How many GPM's is the pump rated for? (what happens when both neighbors do laundry at the same time that you are trying to take a quick shower before going to work...)
Are there water shortages in the dry season? If so, what are the agreed upon "restrictions" on fair use? watering the lawn, car washing etc.
Who pays for pump repairs and who's land is the pump on? Do you have an easement so that you can dig up your water line if part of it on someone elses property breaks.
Be sure and have the water tested for fecal coliforms if plan on using the water for drinking, cooking or brushing your teeth ... or else plan on having gallon jugs sitting around on the kitchen and bathroom countertops and a sign reminding everyone to keep their mouth closed while taking a shower
Those chlorination systems are pricey to purchase- and I doubt the neighbors will share with the cost if they are fine with using the contaminated water.