What is the best heating solution for a room addition in CT. By best I
mean cost, aesthetics, and comfort. It includes a full basement and
measures 16X35. The upstairs will include a kitchen table and a
reading area, while the basement will be the boys hangout, me and my 2
sons quality time. I am leaning towards electric radient floor heating
preferably electric as I do not want to pour concrete with the hot
water option, but am leery of electric usage cost. I would not want to
use baseboards but am willing to consider if unobtrusive. My current
heat is from oil burner with baseboards.

This is  a  very subjective decision

 however warm tiles
://www.google.com/search?hl=en&ie=ISO-8859-1&q=warm+tile

which is cheaper to install then full power floor heating 
://www.google.com/search?hl=en&ie=ISO-8859-1&q=floor+heating

is nice, more pleasant then baseboards.

Key to cost reduction is insulation .

check out www.radiantfloorwarming.com for info on radiant floor,
including estimating how much you will need and how much it will cost
to run.