When it comes to shape, a one carat round brillant looks the largest. So, if you want a bigger presence, no matter what size you get, go for an ideal cut round.
As for the question pertaining to size, I read somewhere that the average size engagement ring throughtout most of the US is a .38. In major cities (e.g. New York) the average size is a 1.6 carat stone. (IMHO that seems a bit large for NY to me. There are many different economics levels living in NYC, so again, it seems large.)
As for your ring personally, get the stone that is the best cut and best color you can afford. If you feel it is a little small, then set it in a Halo Setting. Trust me, you will not be disappointed. Enjoy your search and good luck!