I can understand how you might feel that it makes sense to pay a $1300 mortgage rather than a $1300 rent payment. However, you need to make sure that you have enough money to comfortably cover extra maintenance expenses that may come up with a property in addition to just the mortgage. You don't want to end up owning something and then not being able to fix it. Also, you need to make sure that in addition to not having debt you should have a savings cushion of 3-6 months living expenses so that in case of a temporary hiatus from your income such as job loss, you can keep paying the mortgage. Finally, I would also be asking myself if my life situation were stable enough to be able to hold on to the property for a long time (longer than 5 years) to make sure I don't get stuck having to sell a property in a difficult market, especially if it were purchased with no down payment or a low down payment.
Having said that, contact a mortgage specialist from a local bank in the area you want to move who can talk with you about the qualifications for CHFA, a State of CT financing program, as well as FHA loans. There are other programs with low down payments as well such as HDF.
You can google any of the above terms in Central CT to find the resources you need.
Good luck and congratuations on becoming a newlywed!