Newbie - In most parts of Connecticut, wells and septics are common, and only a few areas - mostly the cities - have city water and city sewer available. So, you may not have a choice.
As for well water, it is recommended that you have the water tested regularly. Most towns will have water testing "events" once or twice a year - I usually pay about $30 each year to have my well water tested, and so far no problems. I do have a whole house filter hooked up to filter out any sediment, and I replace the filter every 3-6 months, as needed. You can also have a company, such as Culligan or even Sears, come out and test your water - of course, then they will try to see you their water systems, such as a water filter, water softener, or a reverse osmosis system.
As for the septic - you need to have it pumped every 2-3 years. Make sure nothing goes down the drain - or down the toilet - other than what is supposed to. You cannot have an in-sink garbage disposal, as the food wastes can clog your septic.
As for laundry or showers, it is recommended that you don't do too many loads of laundry all at once...but this is typically only a problem with septic systems that are at or near capacity.
When buying your new home, you will absolutely want to pay for a septic inspection. It is well worth the money, because if there are problems with the septic, it can be expensive and you want to take this opportunity to try to negotiate for the seller to do the repairs.
Also, you will want your home inspector to test the well water for you, to insure their are no contaminants.