Intel Core i3-2125 Sandy Bridge 3.3GHz LGA 1155 65W Dual-Core Desktop Processor Intel HD Graphics 3000 BX80623I32125 $159.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115093
COOLER MASTER Hyper 212 Plus RR-B10-212P-G1 "Heatpipe Direct Contact" Long Life Sleeve 120mm CPU Cooler Compatible Intel Core i5 & Intel Core i7 $25.99.
http://www.newegg.com/Product/Product.aspx?Item=N82E16835103065
ASRock Z68 Extreme3 Gen3 LGA 1155 Intel Z68 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard $124.99 and a $10 rebate for $114.99.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157271
This comes to $300.97 , I don't know if the 0.97 is going to break you but it is a slightly better package.
If you want to use the stock cooler then you could get this cpu;
Intel Core i5-2300 Sandy Bridge 2.8GHz (3.1GHz Turbo Boost) LGA 1155 95W Quad-Core Desktop Processor Intel HD Graphics 2000 BX80623I52300 $184.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115076
With the MB that is listed the total comes to $299.98 and you would have a much better cpu and the stock cooler should be fine and if you decide to change it later on when you have some more money you can do that. Unless you get an unlocked multiplier you are limited to what you can do for overclocking so the stock heatsink would be fine. All of these choices listed are free shipping.