We lived in East Hampton and had both well and septic. I loved having a well. The water is the best tasting anywhere. You may
find that you will need a filtration system. The area of East Hampton that we lived in had iron in the water. We put in a system to filtrate the iron and soften our water. Some of my immediate neighbors didn't have systems at all. It depends on what you may have in your water and how much of it there is. Some of it depends on personal preference as well. Some of my neighbors didn't have much and didn't mind the metallic taste. The systems will usually run you about 1 to 2 thousand dollars to have installed, depending on what you need and choose. Then you will have maintenance. We had our system serviced once a year at the cost of $75. We also had to add bags of potassium chloride about four times a year. The potassium chloride can be purchased at your local nursery, hardware store, etc. for about $20 dollars a bag. Our water had the perfect texture and taste and I never found a bottled water that could even come close. Again, some of it is personal preference and the house you buy may not need a filtration system at all. This is just something that may come up when you have a well. As far as how deep your well is, that all depends. You could have two houses side by side and one home has a well that is 6 ft deep and another is 12 ft deep. I actually saw this in my neighborhood. If you are building a new home then this can become a big expense as they charge you by the foot after a certain point. Just remember, if you have a pool don't try to fill it with a hose and don't leave a hose going all day and night. One of my neighbors inadvertently left their hose going for about 24 hours and drained their well.
If you have children then their dentist will most likely prescribe flouride pills due to the fact that city water usually has flouride and your well won't. We have since moved and now have city water. I can't tell you how much I miss my well. The city water smells and tastes funny to me, even with filtration. I'm getting used to it but it will never be the same as well water.
In regards to the septic system. We had ours pumped every 1 1/2 to 2 years to avoid any problems. Some people will go as long as 3 years. If you do move to East Hampton I would highly recommend the two local companies, I can't mention their names as it would be advertising. It usually cost us about $150. As the other poster mentioned, it is important that your system is large enough for your home size and family size. Newer homes should be in compliance as the zoning laws are strict in this respect. You really should have a septic inspection as part of your home purchase contract. When the septic is emptied (paid for by the seller) the company doing so can tell you if the septic is the appropriate size. As part of the upkeep of your septic they suggest using finer toilet paper such as Scotts not the fluffy stuff like Charmin Ultra. I was also told to NEVER put bleach down the drain or toilet, such as the bleach cleaning tablets you can buy for your toilet. You should also use bleach in your laundry as little as possible. Bleach kills the good bacteria in your septic system.
I have seen the sewer bills that friends of mine have to pay in surrounding towns and I was always thankful I didn't have that expense. The same goes for water bills. You may have to pay for maintenance but I believe it all evens out in the end.
On a final note, East Hampton was my absolute favorite town to live in CT. Please feel free to DM me with any questions you might have about the area. Best of luck to you!