As you already know its going to vary greatly. But I can try to get you in the ballpark.

I live in a 2100 square foot ranch and I expect to burn 700-800 gallons of oil this winter, but again this could vary. So at the current lovely price of ~$5/gallon around $3500 this year for heat.

My electric bill is fairly consistent around $170/month and I do run AC in the summer...However I have seen people talk about much higher electric bills so this one is super variable because the electric companies seem to just do whatever they want.

If you have city water its going to depend a lot on how many people are in your home but I would say budgeting for 30-45/month is reasonable...highly dependent on how many people are showering, how much laundry, watering gardens etc. If your home has well water it will be a very small bump to your electric bill.

Sorry I can't be more specific. I'm not sure if you already have a home in mind but something I've done for clients is had the sellers provide historical utility bills...especially when dealing with houses with solar because I've seen so many cases of the solar not actually saving the homeowner any money (crazy solar leases).

This is unrelated to utilities and again not sure if you have a home or town in mind... but one thing to keep in mind when working on budget is how variable property tax can be from town to town in CT. This is going to be a massive part of your monthly payment depending on where you land. And is why I encourage clients to shop by monthly payment and NOT purchase price... saying you are preapproved for 300k means almost nothing because 300k in one town could have the same monthly payment as a 400k home in another town purely because of property tax. Happy to delve more into this if you have questions.