I bought the engagement ring and wedding band from a big store (ShaneCo), but I sourced the diamond separately to avoid the markup those stores have on their diamonds.
My priority order was carat and cut, then color, and finally clarity. 1.5 to 2 carat seems to be the sweet spot for a good sized stone. It's not too small and not so big it looks like costume jewelry. Probably a little variance here depending on the setting.
As others have said, cut is important as that determines the how light passes thru the stone and thus the sparkle. Along with getting what jewelers consider "ideal" or "excellent" cut, also check the HCA score. It takes cut one step further to measure the dimensions of the stone to determine brilliance. (
http://www.pricescope.com/tools/hca)
Color is relative. I prefer a colorless stone (F or better), but G-H-I are almost colorless if mounted in a white metal setting. Yellow gold tends to bring out the color in a diamond a little more.
Clarity is important to a point. I went with "eye clean" which is generally SI1 or better. Basically this means you can't see the inclusions without a loupe.