First... The i3 550 (socket 1156) will not work with the Asus p8H61 mobo (socket 1155)
You should get the i3 2100 (Socket 1155) or better. The i3 2100 is a better processor...
Check out the Toms System builder Marathon for December 2011.
They made a $600 PC with an i5 2400.http://www.tomshardware.com/reviews/core-i5-overclock-performance-gaming,3097.html
You can use this as a jumping off point.
They only used 4 gb of RAM which is technically sufficient but RAM is cheap and for just a few dollars more you can double your RAM and never be concerned with having too little RAM. As far as RAM get an 8 GB kit with 2x4Gb of DDR3 1600 Mhz with a 1.5voltage or lower. Choose between reputable brands like G.Skill, Corsair, Kingston...
I've been looking to get this case for a new build for my wife, the XCLIO Godspeed. It has been getting very good reviews.http://www.newegg.com/Product/Product.aspx?Item=N82E16811103035&Tpk=xclio%20godspeed
Cases have a lot to do with personal preference. My rig has a huge ugly case that has excellent cooling capacity. My wife wants something more discreet so next week I am going to get her the XCLIO. Get what you like! you are ther one that has to look at it for a couple of years.
Also if you went with the Tom's H SBM Machine you would get a 6870 in your budget.