I'd take a Phenom II 965 Black edition over an i3 personally. In my opinion theres too big of a price gap between Intel's quad core and dual cores. And the remaining AMD Phenom IIs fall right in the middle of that gap as they are true quad cores. If you can afford the i5 (starting at 180) those would be the best choice, but a Phenom II at the price point is going to offer you better balance for a system outside of gaming.
I'd use Underhill's build, but I'd make the following changes:
CPU- Both the i3 and 965 can handle single player games very well and are about even in performance, but in terms of multiplayer, most games are more CPU intensive, and you may find the i3's 2 cores causes limitations.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103727
Mobo:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157280
Video card: (Same price, slightly better)
http://www.newegg.com/Product/Product.aspx?Item=N82E16814161389
As far as your concern with Newegg, maybe you had a bad experience with them, but honestly, I have ordered from them several times and found them to be incredibly reliable and expedient in their shipping. I'd give them another shot. TigerDirect is equally good. The only online merchant I can say I would avoid would be MicroCenter. They have what seems to be decent prices, but I found the devil is in the details, as they charged me both shipping and sales tax for orders that Newegg or Tiger wouldn't, which made the final price being no cheaper, and the other tradeoff was MicroCenter ships painfully slow. They had my order "processing" for over a week and after 2 phone calls to them and talking to their inept customer support, I cancelled the order. Meanwhile Newegg had my stuff to my door in 2 days.